Question

How do i solve this

Answer 1

$5.\\5^\frac{1}{4}\cdot5^\frac{1}{4}\cdot5^\frac{1}{4}=5^{\frac{1}{4}+\frac{1}{4}+\frac{1}{4}}=5^\frac{3}{4}=\sqrt[4]{5^3}=\sqrt[4]{125}\\\\/\text{used:}\ a^n\cdot a^m=a^{n+m}/\\6.\\\left(5^\frac{1}{4}\right)^6=5^{\frac{1}{4}\cdot6}=5^{\frac{1}{2}\cdot3}=5^\frac{3}{2}=5^{1\frac{1}{2}}=5\sqrt5\\\\/\text{used:}\ (a^n)^m=a^{n\cdot m}/$
$7.\\5^{-\frac{1}{4}}=\dfrac{1}{5^\frac{1}{4}}=\dfrac{1}{\sqrt[4]5}\\\\/\text{used:}\ a^{-n}=\dfrac{1}{a^n}/\\8.\\5^2\cdot5^\frac{1}{4}=5^{2+\frac{1}{4}}=5^{2\frac{1}{4}}=5^\frac{9}{4}=5^2\sqrt[4]5=25\sqrt[4]5$

$a^\frac{m}{n}=\sqrt[n]{a^m}$