{"id":1716,"date":"2020-09-09T10:55:54","date_gmt":"2020-09-09T08:55:54","guid":{"rendered":"http:\/\/matma.com.pl\/?p=1716"},"modified":"2020-09-09T13:57:34","modified_gmt":"2020-09-09T11:57:34","slug":"potegi-notacja-wykladnicza-pierwiastki","status":"publish","type":"post","link":"http:\/\/matma.com.pl\/?p=1716","title":{"rendered":"IV.Pot\u0119gi. Notacja wyk\u0142adnicza. Pierwiastki"},"content":{"rendered":"<p><span style=\"color: #339966;\"><strong><span style=\"font-family: 'book antiqua', palatino, serif;\">Pot\u0119gi<\/span><\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Pot\u0119ga to nic innego jak wielokrotny iloczyn jednakowych czynnik\u00f3w.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a^{1}=a\" alt=\"a^{1}=a\" align=\"absmiddle\" \/>\u00a0pierwsza pot\u0119ga liczby\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a\" alt=\"a\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a^{2}=a\\cdot&amp;space;a\" alt=\"a^{2}=a\\cdot a\" align=\"absmiddle\" \/>\u00a0druga pot\u0119ga liczby\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a\" alt=\"a\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a^{3}=a\\cdot&amp;space;a\\cdot&amp;space;a\" alt=\"a^{3}=a\\cdot a\\cdot a\" align=\"absmiddle\" \/>\u00a0trzecia pot\u0119ga liczby\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a\" alt=\"a\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\vdots\" alt=\"\\vdots\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a^{n}=a\\cdot&amp;space;a\\cdot&amp;space;...\\cdot&amp;space;a\" alt=\"a^{n}=a\\cdot a\\cdot ...\\cdot a\" align=\"absmiddle\" \/>\u00a0n-ta pot\u0119ga liczby\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a\" alt=\"a\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"size-medium wp-image-1370 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pot%C4%99ga1-300x162.png\" sizes=\"(max-width: 300px) 100vw, 300px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pot\u0119ga1-300x162.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pot\u0119ga1.png 319w\" alt=\"\" width=\"300\" height=\"162\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><strong><span style=\"color: #339966;\">n-ta pot\u0119ga<\/span><\/strong>\u00a0liczby. a to iloczyn n czynnik\u00f3w a.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a^{0}=1\" alt=\"a^{0}=1\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"text-decoration: underline;\"><span style=\"font-family: 'book antiqua', palatino, serif;\">Pami\u0119taj, \u017ce pot\u0119gowanie\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?0^{0}\" alt=\"0^{0}\" align=\"absmiddle\" \/>\u00a0nie jest wykonalne!<\/span><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Parzysta pot\u0119ga ka\u017cdej liczby jest liczb\u0105 dodatni\u0105.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?2^{4}=2\\cdot&amp;space;2\\cdot&amp;space;2\\cdot&amp;space;2=16\" alt=\"2^{4}=2\\cdot 2\\cdot 2\\cdot 2=16\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Nieparzysta pot\u0119ga liczby dodatniej jest liczb\u0105 dodatni\u0105.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?5^{3}=5\\cdot&amp;space;5\\cdot&amp;space;5=125\" alt=\"5^{3}=5\\cdot 5\\cdot 5=125\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Parzysta pot\u0119ga liczby ujemnej jest liczb\u0105 dodatni\u0105.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;-\\frac{1}{2}&amp;space;\\right&amp;space;)^{4}=\\left&amp;space;(&amp;space;-\\frac{1}{2}&amp;space;\\right&amp;space;)\\cdot&amp;space;\\left&amp;space;(&amp;space;-\\frac{1}{2}&amp;space;\\right&amp;space;)\\cdot&amp;space;\\left&amp;space;(&amp;space;-\\frac{1}{2}&amp;space;\\right&amp;space;)\\cdot&amp;space;\\left&amp;space;(&amp;space;-\\frac{1}{2}&amp;space;\\right&amp;space;)=\\frac{1}{16}\" alt=\"\\left ( -\\frac{1}{2} \\right )^{4}=\\left ( -\\frac{1}{2} \\right )\\cdot \\left ( -\\frac{1}{2} \\right )\\cdot \\left ( -\\frac{1}{2} \\right )\\cdot \\left ( -\\frac{1}{2} \\right )=\\frac{1}{16}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Nieparzysta pot\u0119ga liczby ujemnej jest liczba ujemn\u0105.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(-0,1&amp;space;\\right&amp;space;)^{3}=\\left&amp;space;(-0,1&amp;space;\\right&amp;space;)\\cdot&amp;space;\\left&amp;space;(-0,1&amp;space;\\right&amp;space;)\\cdot&amp;space;\\left&amp;space;(-0,1&amp;space;\\right&amp;space;)=-0,001\" alt=\"\\left (-0,1 \\right )^{3}=\\left (-0,1 \\right )\\cdot \\left (-0,1 \\right )\\cdot \\left (-0,1 \\right )=-0,001\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #339966;\"><strong><span style=\"font-family: 'book antiqua', palatino, serif;\">Dzia\u0142ania na pot\u0119gach<\/span><\/strong><\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a^{m}\\cdot&amp;space;a^{n}=a^{m+n}\" alt=\"a^{m}\\cdot a^{n}=a^{m+n}\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?3^{2}\\cdot&amp;space;3^{5}=3^{2+5}=3^{7}\" alt=\"3^{2}\\cdot 3^{5}=3^{2+5}=3^{7}\" align=\"absmiddle\" \/><\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a^{m}:&amp;space;a^{n}=a^{m-n}\" alt=\"a^{m}: a^{n}=a^{m-n}\" align=\"absmiddle\" \/>\u00a0 dla\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a\\neq&amp;space;0\" alt=\"a\\neq 0\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?5^{5}:5^{2}=5^{5-2}=5^{3}\" alt=\"5^{5}:5^{2}=5^{5-2}=5^{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(a^{m}&amp;space;\\right&amp;space;)^{n}=a^{m\\cdot&amp;space;n}\" alt=\"\\left (a^{m} \\right )^{n}=a^{m\\cdot n}\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(2^{3}&amp;space;\\right&amp;space;)^{6}=2^{3\\cdot&amp;space;6}=2^{18}\" alt=\"\\left (2^{3} \\right )^{6}=2^{3\\cdot 6}=2^{18}\" align=\"absmiddle\" \/><\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;a\\cdot&amp;space;b&amp;space;\\right&amp;space;)^{n}=a^{n}\\cdot&amp;space;b^{n}\" alt=\"\\left ( a\\cdot b \\right )^{n}=a^{n}\\cdot b^{n}\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(3\\cdot&amp;space;10&amp;space;\\right&amp;space;)^{3}=3^{3}\\cdot&amp;space;10^{3}=27\\cdot&amp;space;1000=27000\" alt=\"\\left (3\\cdot 10 \\right )^{3}=3^{3}\\cdot 10^{3}=27\\cdot 1000=27000\" align=\"absmiddle\" \/><\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;a:b&amp;space;\\right&amp;space;)^{n}=a^{n}:b^{n}\" alt=\"\\left ( a:b \\right )^{n}=a^{n}:b^{n}\" align=\"absmiddle\" \/>\u00a0dla\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?b\\neq&amp;space;0\" alt=\"b\\neq 0\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(10:5&amp;space;\\right&amp;space;)^{3}=10^{3}:5^{3}=1000:125=8\" alt=\"\\left (10:5 \\right )^{3}=10^{3}:5^{3}=1000:125=8\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Oczywi\u015bcie znak dzielenia mo\u017cemy zast\u0105pi\u0107 kresk\u0105 u\u0142amkow\u0105.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif; color: #339966;\"><strong>Notacja wyk\u0142adnicza<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Notacja wyk\u0142adnicza to notacja naukowa. S\u0142u\u017cy do zapisywania bardzo du\u017cych lub bardzo ma\u0142ych wielko\u015bci. Jest to iloczyn liczby wi\u0119kszej lub r\u00f3wnej 1, ale mniejszej od 10 i pot\u0119gi liczby 10.<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a\\cdot&amp;space;10^{n}{\\color{DarkGreen}&amp;space;}\" alt=\"a\\cdot 10^{n}{\\color{DarkGreen} }\" width=\"80\" height=\"21\" align=\"absmiddle\" \/> \u00a0 \u00a0 \u00a0 \u00a0 dla\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <img decoding=\"async\" class=\"\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a\\geq&amp;space;1\\;&amp;space;\\;&amp;space;i\\;&amp;space;\\;&amp;space;a%3C&amp;space;10\" alt=\"a\\geq 1\\; \\; i\\; \\; a&lt; 10\" width=\"166\" height=\"19\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Spr\u00f3bujmy zapisa\u0107 du\u017c\u0105 i ma\u0142\u0105 liczb\u0119 w postaci notacji wyk\u0142adniczej.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?3400000=3,4\\cdot&amp;space;10^{^{6}}\" alt=\"3400000=3,4\\cdot 10^{^{6}}\" align=\"absmiddle\" \/>\u00a0( przesuwamy przecinek o 6 miejsc w lewo)<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?0,000053=5,3\\cdot&amp;space;10^{-5}\" alt=\"0,000053=5,3\\cdot 10^{-5}\" align=\"absmiddle\" \/>\u00a0(przesuwamy przecinek o 5 miejsc w prawo)<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif; color: #339966;\"><strong>Pierwiastki<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Pierwiastkowanie to dzia\u0142anie odwrotne do pot\u0119gowania.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #339966;\"><strong>Pierwiastek kwadratowy<\/strong><\/span>\u00a0(pierwiastek drugiego stopnia) z danej liczby nieujemnej a jest to liczba nieujemna b taka, \u017ce jej kwadrat jest r\u00f3wny a. Liczb\u0119 a pod pierwiastkiem nazywamy<span style=\"color: #339966;\">\u00a0<strong>liczba podpierwiastkow\u0105<\/strong><\/span>.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-1721 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/pierwiatek-kwadratowy-opisyy-300x125.png\" alt=\"\" width=\"356\" height=\"148\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/pierwiatek-kwadratowy-opisyy-300x125.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/pierwiatek-kwadratowy-opisyy.png 519w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">M\u00f3wi\u0105c pierwiastek mamy na my\u015bli pierwiastek kwadratowy. Najcz\u0119\u015bciej zapisujemy symbolem\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{&amp;space;\\:&amp;space;\\:&amp;space;}\" alt=\"\\sqrt{ \\: \\: }\" align=\"absmiddle\" \/>\u00a0. Trzeba pami\u0119ta\u0107, \u017ce jest on jednoznaczny z zapisem\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt[2]{&amp;space;\\:&amp;space;\\:&amp;space;}\" alt=\"\\sqrt[2]{ \\: \\: }\" align=\"absmiddle\" \/>.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1366 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pierwiastek-2.png\" alt=\"\" width=\"100\" height=\"50\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1362 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pierwiastek-300x122.png\" alt=\"\" width=\"322\" height=\"131\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1363 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pierwiastek1-300x39.png\" sizes=\"(max-width: 346px) 100vw, 346px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pierwiastek1-300x39.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pierwiastek1-600x80.png 600w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pierwiastek1.png 619w\" alt=\"\" width=\"346\" height=\"45\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Przyk\u0142ady:<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{4}=2\\;&amp;space;\\;&amp;space;bo\\;&amp;space;\\;&amp;space;2^{2}=4\" alt=\"\\sqrt{4}=2\\; \\; bo\\; \\; 2^{2}=4\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{1,69}=1,3\\;&amp;space;\\;&amp;space;bo\\;&amp;space;\\;&amp;space;\\left&amp;space;(1,3&amp;space;\\right&amp;space;)^{2}=1,69\" alt=\"\\sqrt{1,69}=1,3\\; \\; bo\\; \\; \\left (1,3 \\right )^{2}=1,69\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{0}=0\\;&amp;space;\\;&amp;space;bo\\;&amp;space;\\;&amp;space;0^{2}=0\" alt=\"\\sqrt{0}=0\\; \\; bo\\; \\; 0^{2}=0\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{\\frac{1}{64}}=\\frac{1}{8}\\;&amp;space;\\;&amp;space;bo\\;&amp;space;\\;&amp;space;\\left&amp;space;(&amp;space;\\frac{1}{8}&amp;space;\\right&amp;space;)^{2}=\\frac{1}{64}\" alt=\"\\sqrt{\\frac{1}{64}}=\\frac{1}{8}\\; \\; bo\\; \\; \\left ( \\frac{1}{8} \\right )^{2}=\\frac{1}{64}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #339966;\"><strong>Pierwiastek sze\u015bcienny<\/strong><\/span>\u00a0(pierwiastek trzeciego stopnia) z danej liczby nieujemnej a jest to liczba nieujemna b taka, \u017ce jej sze\u015bcian (trzecia pot\u0119ga) jest r\u00f3wny a.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1367 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pierwiastek-sze%C5%9Bcien-300x101.png\" sizes=\"(max-width: 339px) 100vw, 339px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pierwiastek-sze\u015bcien-300x101.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pierwiastek-sze\u015bcien.png 480w\" alt=\"\" width=\"339\" height=\"114\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1364 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pierwiastek-sze%C5%9Bcienny-1-300x60.png\" sizes=\"(max-width: 201px) 100vw, 201px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pierwiastek-sze\u015bcienny-1-300x60.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pierwiastek-sze\u015bcienny-1.png 355w\" alt=\"\" width=\"201\" height=\"40\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Przyk\u0142ady:<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt[3]{8}=2\\;&amp;space;\\;&amp;space;bo\\;&amp;space;\\;&amp;space;2^{3}=8\" alt=\"\\sqrt[3]{8}=2\\; \\; bo\\; \\; 2^{3}=8\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt[3]{-125}=-5\\;&amp;space;\\;&amp;space;bo\\;&amp;space;\\;&amp;space;\\left&amp;space;(-5&amp;space;\\right&amp;space;)^{3}=-125\" alt=\"\\sqrt[3]{-125}=-5\\; \\; bo\\; \\; \\left (-5 \\right )^{3}=-125\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt[3]{0}=0\\;&amp;space;\\;&amp;space;bo\\;&amp;space;\\;&amp;space;0^{3}=0\" alt=\"\\sqrt[3]{0}=0\\; \\; bo\\; \\; 0^{3}=0\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt[3]{\\frac{1}{27}}=\\frac{1}{3}\\;&amp;space;\\;&amp;space;bo\\;&amp;space;\\;&amp;space;\\left&amp;space;(&amp;space;\\frac{1}{3}&amp;space;\\right&amp;space;)^{3}=\\frac{1}{27}\" alt=\"\\sqrt[3]{\\frac{1}{27}}=\\frac{1}{3}\\; \\; bo\\; \\; \\left ( \\frac{1}{3} \\right )^{3}=\\frac{1}{27}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><strong><span style=\"font-family: 'book antiqua', palatino, serif; color: #339966;\">Dzia\u0142ania na pierwiastkach:<\/span><\/strong><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{a\\cdot&amp;space;b}=\\sqrt{a}\\cdot&amp;space;\\sqrt{b}\" alt=\"\\sqrt{a\\cdot b}=\\sqrt{a}\\cdot \\sqrt{b}\" align=\"absmiddle\" \/>\u00a0 \u00a0dla\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a\\geq&amp;space;0\\;&amp;space;i&amp;space;\\;&amp;space;b\\geq&amp;space;0\" alt=\"a\\geq 0\\; i \\; b\\geq 0\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{2500}=\\sqrt{25\\cdot&amp;space;100}=\\sqrt{25}\\cdot&amp;space;\\sqrt{100}=5\\cdot&amp;space;10=50\" alt=\"\\sqrt{2500}=\\sqrt{25\\cdot 100}=\\sqrt{25}\\cdot \\sqrt{100}=5\\cdot 10=50\" align=\"absmiddle\" \/><\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{\\frac{a}{b}}=\\frac{\\sqrt{a}}{\\sqrt{b}}\" alt=\"\\sqrt{\\frac{a}{b}}=\\frac{\\sqrt{a}}{\\sqrt{b}}\" align=\"absmiddle\" \/>\u00a0 dla\u00a0<img decoding=\"async\" style=\"box-sizing: border-box; max-width: 100%; height: auto; vertical-align: top; margin-bottom: 0px;\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a\\geq&amp;space;0\\;&amp;space;i&amp;space;\\;&amp;space;b%3E&amp;space;0\" alt=\"a\\geq 0\\; i \\; b&gt; 0\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{0,04}=\\sqrt{\\frac{4}{100}}=\\frac{\\sqrt{4}}{\\sqrt{100}}=\\frac{\\cancel{2}}{\\cancel{10}}=\\frac{1}{5}=0,2\" alt=\"\\sqrt{0,04}=\\sqrt{\\frac{4}{100}}=\\frac{\\sqrt{4}}{\\sqrt{100}}=\\frac{\\cancel{2}}{\\cancel{10}}=\\frac{1}{5}=0,2\" align=\"absmiddle\" \/><\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt[3]{a\\cdot&amp;space;b}=\\sqrt[3]{a}\\cdot&amp;space;\\sqrt[3]{b}\" alt=\"\\sqrt[3]{a\\cdot b}=\\sqrt[3]{a}\\cdot \\sqrt[3]{b}\" align=\"absmiddle\" \/>\u00a0 dla dowolnych a i b<\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt[3]{64000}=\\sqrt[3]{64\\cdot&amp;space;1000}=\\sqrt[3]{64}\\cdot&amp;space;\\sqrt[3]{1000}=4\\cdot&amp;space;10=40\" alt=\"\\sqrt[3]{64000}=\\sqrt[3]{64\\cdot 1000}=\\sqrt[3]{64}\\cdot \\sqrt[3]{1000}=4\\cdot 10=40\" align=\"absmiddle\" \/><\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt[3]{\\frac{a}{b}}=\\frac{\\sqrt[3]{a}}{\\sqrt[3]{b}}\" alt=\"\\sqrt[3]{\\frac{a}{b}}=\\frac{\\sqrt[3]{a}}{\\sqrt[3]{b}}\" align=\"absmiddle\" \/>\u00a0 dla dowolnego a i\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?b\\neq&amp;space;0\" alt=\"b\\neq 0\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt[3]{-0,125}=\\sqrt[3]{-\\frac{125}{1000}}=-\\frac{\\sqrt[3]{125}}{\\sqrt[3]{1000}}=-\\frac{\\cancel{5}}{\\cancel{10}}=-\\frac{1}{2}=-0,5\" alt=\"\\sqrt[3]{-0,125}=\\sqrt[3]{-\\frac{125}{1000}}=-\\frac{\\sqrt[3]{125}}{\\sqrt[3]{1000}}=-\\frac{\\cancel{5}}{\\cancel{10}}=-\\frac{1}{2}=-0,5\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Przypomnijmy sobie jeszcze<span style=\"color: #339966;\"><strong> regu\u0142y kolejno\u015bci wykonywania dzia\u0142a\u0144:<\/strong><\/span><\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #339966;\"><strong>nawiasy<\/strong><\/span>\u00a0informuj\u0105 nas o tym, \u017ce dzia\u0142ania w nich wykonujemy w pierwszej kolejno\u015bci;<\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #339966;\"><strong>pot\u0119gowanie i pierwiastkowanie<\/strong>\u00a0<\/span>ma pierwsze\u0144stwo przed mno\u017ceniem, dzieleniem, dodawaniem i odejmowaniem;<\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #339966;\"><strong>mno\u017cenie i dzielenie<\/strong><\/span>\u00a0s\u0105 to dzia\u0142ania, kt\u00f3re wykonujemy przed dodawaniem i odejmowaniem, ale gdy wyst\u0119puje mno\u017cenie obok dzielenia w\u00f3wczas wykonujemy je po kolei, tak jak wyst\u0119puj\u0105 \u2013 od lewej strony;<\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #339966;\"><strong>dodawanie i odejmowanie<\/strong><\/span>\u00a0dzia\u0142ania, kt\u00f3re wykonujemy na samym ko\u0144cu, natomiast gdy wyst\u0119puj\u0105 jedno obok drugiego to wykonujemy je po kolei, tak jak wyst\u0119puj\u0105 \u2013 od lewej strony.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Zadanie 1<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Oblicz:<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;0,4&amp;space;\\right&amp;space;)^{2}\" alt=\"\\left ( 0,4 \\right )^{2}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{1}{5}&amp;space;\\right&amp;space;)^{3}\" alt=\"\\left ( \\frac{1}{5} \\right )^{3}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;-0,3&amp;space;\\right&amp;space;)^{3}\" alt=\"\\left ( -0,3 \\right )^{3}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(-\\frac{2}{5}&amp;space;\\right&amp;space;)^{2}\" alt=\"\\left (-\\frac{2}{5} \\right )^{2}\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ol>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Zadanie 2<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Oblicz:<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;3,5&amp;space;\\right&amp;space;)^{2}\\cdot&amp;space;2^{2}\" alt=\"\\left ( 3,5 \\right )^{2}\\cdot 2^{2}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?(-1)^{5}:(-1)\" alt=\"(-1)^{5}:(-1)\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(\\frac{2}{5}&amp;space;\\right&amp;space;)^{3}:(0,4)^{2}\" alt=\"\\left (\\frac{2}{5} \\right )^{3}:(0,4)^{2}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(\\left&amp;space;(\\frac{2}{3}&amp;space;\\right&amp;space;)^{2}&amp;space;\\right&amp;space;)^{2}\" alt=\"\\left (\\left (\\frac{2}{3} \\right )^{2} \\right )^{2}\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ol>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">zadanie 3<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Oblicz:<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{64}\" alt=\"\\sqrt{64}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt[3]{-64}\" alt=\"\\sqrt[3]{-64}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{\\frac{49}{121}}\" alt=\"\\sqrt{\\frac{49}{121}}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt[3]{-0,216}\" alt=\"\\sqrt[3]{-0,216}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{0,0121}\" alt=\"\\sqrt{0,0121}\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ol>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Zadanie 4<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Oblicz:<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{8}\" alt=\"\\sqrt{8}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{125}\" alt=\"\\sqrt{125}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt{20}\" alt=\"\\sqrt{20}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt[3]{128}\" alt=\"\\sqrt[3]{128}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\sqrt[3]{-54}\" alt=\"\\sqrt[3]{-54}\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ol>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Zadanie 5<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Oblicz:<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?2\\sqrt{2}+\\sqrt{8}\" alt=\"2\\sqrt{2}+\\sqrt{8}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?10\\sqrt[3]{54}-20\\sqrt[3]{3}\" alt=\"10\\sqrt[3]{54}-20\\sqrt[3]{3}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?5\\sqrt[3]{-125}+25\\sqrt[3]{5}\" alt=\"5\\sqrt[3]{-125}+25\\sqrt[3]{5}\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ol>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Zadanie 6<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Oblicz:<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{0,99:3-1\\cdot&amp;space;1,5}{\\frac{4}{7}}&amp;space;\\right&amp;space;)^{0}\" alt=\"\\left ( \\frac{0,99:3-1\\cdot 1,5}{\\frac{4}{7}} \\right )^{0}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(\\sqrt[3]{-64}+3\\cdot&amp;space;\\frac{2}{\\sqrt{9}}&amp;space;\\right&amp;space;)^{2}\" alt=\"\\left (\\sqrt[3]{-64}+3\\cdot \\frac{2}{\\sqrt{9}} \\right )^{2}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?2\\sqrt{2}+\\sqrt{8}\" alt=\"2\\sqrt{2}+\\sqrt{8}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(3\\sqrt{5}-4\\sqrt[3]{-125}&amp;space;\\right&amp;space;)\\cdot&amp;space;2-2\" alt=\"\\left (3\\sqrt{5}-4\\sqrt[3]{-125} \\right )\\cdot 2-2\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Pot\u0119gi Pot\u0119ga to nic innego jak wielokrotny iloczyn jednakowych czynnik\u00f3w. \u00a0pierwsza pot\u0119ga liczby\u00a0 \u00a0druga pot\u0119ga liczby\u00a0 \u00a0trzecia pot\u0119ga liczby\u00a0 \u00a0n-ta pot\u0119ga liczby\u00a0 n-ta pot\u0119ga\u00a0liczby. a to iloczyn n czynnik\u00f3w a. Pami\u0119taj, \u017ce pot\u0119gowanie\u00a0\u00a0nie jest wykonalne! Parzysta pot\u0119ga ka\u017cdej liczby jest liczb\u0105 dodatni\u0105. Nieparzysta pot\u0119ga liczby dodatniej jest liczb\u0105 dodatni\u0105. Parzysta pot\u0119ga liczby ujemnej jest liczb\u0105 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[45],"tags":[],"class_list":["post-1716","post","type-post","status-publish","format-standard","hentry","category-egzamin-osmoklasisty"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>IV.Pot\u0119gi. Notacja wyk\u0142adnicza. Pierwiastki - Matma.com.pl<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/matma.com.pl\/?p=1716\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"IV.Pot\u0119gi. Notacja wyk\u0142adnicza. Pierwiastki - Matma.com.pl\" \/>\n<meta property=\"og:description\" content=\"Pot\u0119gi Pot\u0119ga to nic innego jak wielokrotny iloczyn jednakowych czynnik\u00f3w. \u00a0pierwsza pot\u0119ga liczby\u00a0 \u00a0druga pot\u0119ga liczby\u00a0 \u00a0trzecia pot\u0119ga liczby\u00a0 \u00a0n-ta pot\u0119ga liczby\u00a0 n-ta pot\u0119ga\u00a0liczby. a to iloczyn n czynnik\u00f3w a. Pami\u0119taj, \u017ce pot\u0119gowanie\u00a0\u00a0nie jest wykonalne! Parzysta pot\u0119ga ka\u017cdej liczby jest liczb\u0105 dodatni\u0105. Nieparzysta pot\u0119ga liczby dodatniej jest liczb\u0105 dodatni\u0105. Parzysta pot\u0119ga liczby ujemnej jest liczb\u0105 [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/matma.com.pl\/?p=1716\" \/>\n<meta property=\"og:site_name\" content=\"Matma.com.pl\" \/>\n<meta property=\"article:published_time\" content=\"2020-09-09T08:55:54+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-09-09T11:57:34+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/latex.codecogs.com\/gif.latex?a1=a\" \/>\n<meta name=\"author\" content=\"lucynabartczak99\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"lucynabartczak99\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/matma.com.pl\/?p=1716#article\",\"isPartOf\":{\"@id\":\"https:\/\/matma.com.pl\/?p=1716\"},\"author\":{\"name\":\"lucynabartczak99\",\"@id\":\"https:\/\/matma.com.pl\/#\/schema\/person\/b54229c3e035dea49ef8c166c5c63f1e\"},\"headline\":\"IV.Pot\u0119gi. 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Notacja wyk\u0142adnicza. Pierwiastki - Matma.com.pl","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/matma.com.pl\/?p=1716","og_locale":"pl_PL","og_type":"article","og_title":"IV.Pot\u0119gi. Notacja wyk\u0142adnicza. Pierwiastki - Matma.com.pl","og_description":"Pot\u0119gi Pot\u0119ga to nic innego jak wielokrotny iloczyn jednakowych czynnik\u00f3w. \u00a0pierwsza pot\u0119ga liczby\u00a0 \u00a0druga pot\u0119ga liczby\u00a0 \u00a0trzecia pot\u0119ga liczby\u00a0 \u00a0n-ta pot\u0119ga liczby\u00a0 n-ta pot\u0119ga\u00a0liczby. a to iloczyn n czynnik\u00f3w a. Pami\u0119taj, \u017ce pot\u0119gowanie\u00a0\u00a0nie jest wykonalne! Parzysta pot\u0119ga ka\u017cdej liczby jest liczb\u0105 dodatni\u0105. Nieparzysta pot\u0119ga liczby dodatniej jest liczb\u0105 dodatni\u0105. 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