Question

Evaluate $\frac{ \sqrt[4]{9} \sqrt{9} }{ \sqrt[4]{9^5} }$

Answer 1

$\Large \frac{ \sqrt[4]{9} \sqrt{9} }{ \sqrt[4]{9^5} }$

$\Large \frac{ 9^{1/4} 9^{1/2} }{ 9^{5/4} }$

$\Large \frac{ 9^{1/4+1/2} }{ 9^{5/4} }$

$\Large \frac{ 9^{3/4} }{ 9^{5/4} }$

$\Large 9^{3/4-5/4}$

$\Large 9^{-2/4}$

$\Large 9^{-1/2}$

$\Large \frac{1}{\sqrt{9}}$

$\Large \frac{1}{3}$

The final answer is $\Large \frac{1}{3}$