Question

transforme as potencias de expoentes fracionarios em radicais:

a) 9³/²
b) 64⅔
c) 81‐⁰'²⁵
d) (16⁵/⁴)⅖​

Answer 1

$\Huge\boxed{\begin{array}{l}\underline{\sf Pot\hat encia\,de\,expoente\,racional}\\\\\rm \sqrt[\rm n]{\rm a^m}=a^{\frac{m}{n}}\end{array}}$

$\large\boxed{\begin{array}{l}\sf a)~\rm 9^{\frac{3}{2}}=\sqrt{9^3}\\\sf b)~\rm 64^{\frac{2}{3}}=\sqrt[\rm3]{\rm 64^2}\\\sf c)~\rm81^{-0,25}=81^{-\frac{1}{4}}=\dfrac{1}{\sqrt[\rm4]{81}}\\\rm81^{-0,25=}\dfrac{1}{\sqrt[\rm4]{81}}\cdot\dfrac{\sqrt[\rm4]{\rm 81^3}}{\sqrt[\rm4]{\rm 81^3}}\\\\\rm 81^{-0,25}=\dfrac{\sqrt[\rm4]{81^3}}{81}\end{array}}$

$\large\boxed{\begin{array}{l}\sf d)~\rm (16^{\frac{5}{4}})^{\frac{2}{5}}=16^{\frac{\backslash\!\!\!5\cdot\diagup\!\!\!2^1}{\diagup\!\!\!4_2\cdot\backslash\!\!\!5}}\\\rm (16^{\frac{5}{4}})^{\frac{2}{5}}=16^{\frac{1}{2}}=\sqrt{16}\end{array}}$