Question 337649
Take each number to the 30th power.
{{{1^30=1}}}
{{{(2^(1/2))^30=2^15}}}
{{{(3^(1/3))^30=3^10}}}
{{{(4^(1/4))^30=4^(15/2)=2^15}}}
{{{(5^(1/5))^30=5^6}}}
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{{{27>25}}}
{{{3^3>5^2}}}
{{{(3^3)^3>(5^2)^3}}}
{{{3^9>5^6}}}
So then 
{{{3^10>5^6}}}
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{{{9>8}}}
{{{3*3>2*2*2}}}
{{{3^2>2^3}}}
{{{(3^2)^5>(2^3)^5}}}
So then
{{{3^10>2^15}}}
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{{{32>25}}}
{{{2^5>5^2}}}
{{{(2^5)^3>(5^2)^3}}}
So then
{{{2^15>5^6}}}
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Finally put it all together.
From largest to smallest.
{{{3^10}}}
{{{2^15=4^(15/2)}}}
{{{5^6}}}
{{{1^30}}}
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.
{{{3^(1/3)}}}
{{{2^(1/2)=4^(1/4)}}}
{{{5^(1/5)}}}
{{{1}}}