Which one is greater $\left(5/2\right)^{2/5}$ or $\left(7/2\right)^{2/7}$? I have a question here: 
Which of $\left(5/2\right)^{2/5}$ and $\left(7/2\right)^{2/7}$ is greater?
I tried comparison by the function $y=x^{1/x}$ and found the derivative as follows 
$$\frac{\partial y}{\partial x}=\frac{1}{x}(x^{\frac{1}{x}-1})+x^{1/x}\ln x=x^{1/x}(1/x^2+\ln x)$$
I got stuck here, what to do next?
My teacher told me the answer is $\left(5/2\right)^{2/5}$. I want to know how it is. 

Raising both numbers to the power $35/2$ and multiplying both by $2^7$ shows that
$$(5/2)^{2/5}>(7/2)^{2/7}\qquad\Leftrightarrow\qquad(5/2)^7>(7/2)^5\qquad\Leftrightarrow\qquad5^7>2^2\cdot7^5.$$
The latter inequality is not hard to check by hand.
