Potęga o wykładniku wymiernym m przez n

Potęga o wykładniku wymiernym m przez n

• \left.\mleft.27\mright.\right.^{\mleft.\frac{\textcolor{#005FD4}{2}}{\textcolor{#E94D00}{3}}\mright.}=\left.\mleft.\left(\sqrt[{\textcolor{#E94D00}{3}}]{27}\right)\mright.\right.^{\mleft.\textcolor{#005FD4}{2}\mright.}=\left.\mleft.3\mright.\right.^{\mleft.\textcolor{#005FD4}{2}\mright.}=9 2723  =  (3√27)2  =  32  =  9
• \left.\mleft.121\mright.\right.^{\mleft.\frac{\textcolor{#005FD4}{3}}{\textcolor{#E94D00}{2}}\mright.}=\sqrt[{\textcolor{#E94D00}{2}}]{\left.\mleft.121\mright.\right.^{\mleft.\textcolor{#005FD4}{3}\mright.}}=\left.\mleft.\left(\sqrt[{\textcolor{#E94D00}{2}}]{121}\right)\mright.\right.^{\mleft.\textcolor{#005FD4}{3}\mright.}= 12132  =  2√1213  =  (2√121)3  =
  =\left.\mleft.11\mright.\right.^{\mleft.\textcolor{#005FD4}{3}\mright.}=1331 =  113  =  1331
• \left.\mleft.243\mright.\right.^{\mleft.\frac{\textcolor{#005FD4}{3}}{\textcolor{#E94D00}{5}}\mright.}=\left.\mleft.\left(\sqrt[{\textcolor{#E94D00}{5}}]{243}\right)\mright.\right.^{\mleft.\textcolor{#005FD4}{3}\mright.}=\left.\mleft.3\mright.\right.^{\mleft.\textcolor{#005FD4}{3}\mright.}=27 24335  =  (5√243)3  =  33  =  27
• \left.\mleft.13\mright.\right.^{\mleft.\frac{\textcolor{#005FD4}{3}}{\textcolor{#E94D00}{2}}\mright.}=\sqrt[{\textcolor{#E94D00}{2}}]{\left.\mleft.13\mright.\right.^{\mleft.\textcolor{#005FD4}{3}\mright.}}=\sqrt[{2}]{\left.\mleft.13\mright.\right.^{\mleft.2\mright.}\cdot 13}= 1332  =  2√133  =  2√132 ⋅ 13  =
  =13\sqrt[{\textcolor{#E94D00}{2}}]{13} =  132√13
• \left.\mleft.a\mright.\right.^{\mleft.\frac{\textcolor{#005FD4}{\operatorname{m}}}{\textcolor{#E94D00}{n}}\mright.}=\sqrt[{\textcolor{#E94D00}{n}}]{\left.\mleft.a\mright.\right.^{\mleft.\textcolor{#005FD4}{\operatorname{m}}\mright.}}=\left.\mleft.\left(\sqrt[{\textcolor{#E94D00}{n}}]{a}\right)\mright.\right.^{\mleft.\textcolor{#005FD4}{\operatorname{m}}\mright.} amn  =  n√am  =  (n√a)m , gdy a\left.\right.{{\fontfamily{ams}\geqslant \left.\right.}}0 a ⩾  0
• Wyznaczanie potęgi o wykładniku \frac{\operatorname{m}}{n} mn to obliczanie pierwiastka stopnia n n z potęgi o wykładniku \operatorname{m} m .