m Over n

A power like ${25}^{\frac{3}{2}}$ has two jobs. Split the exponent: 3/2 is 1/2 times 3, so by the power of a power rule ${25}^{\frac{3}{2}} = {\left({25}^{\frac{1}{2}}\right)}^{3}$. The bottom of the fraction says which root to take, and the top says which power to raise it to.

$${25}^{\frac{3}{2}} = {\left({25}^{\frac{1}{2}}\right)}^{3} = {5}^{3} = 125$$

In general, for a not negative, ${a}^{\frac{m}{n}} = {\left({a}^{\frac{1}{n}}\right)}^{m}$: the nth root first, then the power m. You could do the power first, ${25}^{3} = 15625$, and then take the square root of 15625. That gives 125 too, since both orders reach the same exponent. But the root first keeps the numbers small enough to do in your head.