what integer is equivalent to 25^3/2

The number reads as 25 to the power of (3/2), which simplifies to
√
15625
.
When an exponent is a fraction, the denominator of the fraction becomes the root. We can take the denominator of 2 and make it the square root, so the square root of
25
3
.
25
3
2

=
√
25
3

Then simplify and solve.
=
√
25
⋅
25
⋅
25

=
√
15625

=
160.0781059