<s>[INST] 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!
 [/INST] Well raise both numbers to the power of $20$
That is 
$$\large{(15^\frac{1}{20})^{20} = 15^\frac{20}{20} = 15}$$
Now $$\large{(20^\frac{1}{15})^{20} = 20^\frac{20}{15} = 20^\frac{4}{3} = 20^{1.333..}}$$
which is greater ? $\large{15}$ or $\large{20^{1.333...}}$
Clearly , it is $\large{20^{1.333..}}$ because $\large{20^{1.333} > 20^1 > 15}$ and so this means that $\large{20^\frac{1}{15} >15^\frac{1}{20}}$
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