How to find out the greater number from $15^{1/20}$ and $20^{1/15}$? I have two numbers $15^{\frac{1}{20}}$ & $20^{\frac{1}{15}}$. 
How to find out the greater number out of above two?
I am in 12th grade. Thanks for help!

This is just another way of looking at alkabary's proof.
\begin{align}
   \left[ \dfrac{20^{\frac{1}{15}}}
         {15^{\frac{1}{20}}} \right]^{20}
   &=\dfrac{20^{\frac 43}}{15} \\
   &= \dfrac 43 20^{\frac 13} \\
   &> \dfrac 43 \cdot 2 \\
   &> 1
\end{align}
$\left[ \dfrac{20^{\frac{1}{15}}}
         {15^{\frac{1}{20}}} \right]^{20} > 1
 \implies \dfrac{20^{\frac{1}{15}}} {15^{\frac{1}{20}}} > 1
 \implies 20^{\frac{1}{15}} > 15^{\frac{1}{20}}$
