Wprowadzenie do pot\u0119gowania<\/p>\n\n\n
Pot\u0119gowanie to operacja matematyczna, kt\u00f3ra polega na mno\u017ceniu liczby przez sam\u0105 siebie okre\u015blon\u0105 ilo\u015b\u0107 razy. Je\u015bli mamy liczb\u0119 \\(a\\) i chcemy j\u0105 podnie\u015b\u0107 do pot\u0119gi \\(n\\), zapisujemy to jako $$\\(a^n\\)$$.<\/p>\n\r\n<\/div>\n\n
\\(a^0 = 1\\) dla ka\u017cdej liczby \\(a \\neq 0\\).<\/p>\n\r\n<\/div>\n\n
\\(2^0 = 1\\), \\(5^0 = 1\\), \\((-3)^0 = 1\\).<\/p>\n\r\n<\/div>\n\n
\\(a^1 = a\\).<\/p>\n\r\n<\/div>\n\n
\\(2^1 = 2\\), \\(5^1 = 5\\), \\((-3)^1 = -3\\).<\/p>\n\r\n<\/div>\n\n
\\(a^{-n} = \\frac{1}{a^n}\\).<\/p>\n\r\n<\/div>\n\n
\\(5^{-4} = \\frac{1}{625}\\), \\((-3)^{-8} = \\frac{1}{6561}\\).<\/p>\n\r\n<\/div>\n\n
\\(\\left(\\frac{a}{b}\\right)^{-n} = \\left(\\frac{b}{a}\\right)^n\\).<\/p>\n\r\n<\/div>\n\n
\\(\\left(\\frac{2}{3}\\right)^{-1} = \\frac{3}{2}\\), \\(\\left(\\frac{1}{2}\\right)^{-3} = 8\\).<\/p>\n\r\n<\/div>\n\n
\\(a^{\\frac{1}{n}} = \\sqrt[n]{a}\\).<\/p>\n\r\n<\/div>\n\n
\\(9^{\\frac{1}{2}} = \\sqrt{9} = 3\\), \\(8^{\\frac{1}{3}} = \\sqrt[3]{8} = 2\\).<\/p>\n\r\n<\/div>\n\n
\\(a^{\\frac{m}{n}} = \\sqrt[n]{a^m}\\).<\/p>\n\r\n<\/div>\n\n
\\(9^{\\frac{3}{2}} = (\\sqrt{9})^3 = 27\\).<\/p>\n\r\n<\/div>\n\n
\\(a^r \\cdot a^s = a^{r+s}\\).<\/p>\n\r\n<\/div>\n\n
\\(2^3 \\cdot 2^5 = 2^{8}\\).<\/p>\n\r\n<\/div>\n\n
\\(\\frac{a^r}{a^s} = a^{r-s}\\).<\/p>\n\r\n<\/div>\n\n
\\(\\frac{2^5}{2^3} = 2^{2}\\).<\/p>\n\r\n<\/div>\n\n
\\((a^r)^s = a^{r \\cdot s}\\).<\/p>\n\r\n<\/div>\n\n
\\((2^3)^4 = 2^{12}\\).<\/p>\n\r\n<\/div>\n\n
\\((a \\cdot b)^r = a^r \\cdot b^r\\).<\/p>\n\r\n<\/div>\n\n
\\((3\\sqrt{5})^2 = 45\\).<\/p>\n\r\n<\/div>\n\n
\\(\\left(\\frac{a}{b}\\right)^r = \\frac{a^r}{b^r}\\).<\/p>\n\r\n<\/div>\n\n
\\(\\left(\\frac{3}{5}\\right)^2 = \\frac{9}{25}\\).<\/p>\n\r\n<\/div>","protected":false},"excerpt":{"rendered":"
Wprowadzenie do pot\u0119gowania<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[106],"tags":[],"class_list":["post-171","post","type-post","status-publish","format-standard","hentry","category-matematyka"],"_links":{"self":[{"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/posts\/171","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/comments?post=171"}],"version-history":[{"count":4,"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/posts\/171\/revisions"}],"predecessor-version":[{"id":763,"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/posts\/171\/revisions\/763"}],"wp:attachment":[{"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/media?parent=171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/categories?post=171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kierunekmatura.pl\/blog\/wp-json\/wp\/v2\/tags?post=171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}