Question

What integer is equivalent to 25 3/2

Answer 1

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

Answer 2

If this was intended to be 25^(3/2), then you can either apply the 3rd power or the second root first:

25^(3/2) = sqrt( 25^3 ) OR 25^(3/2) = ( sqrt(25) )^3

Personally, I’d go with the second approach, because I know sqrt(25) = 5 and I know 5^3 = 125

You could do sqrt( 25^3 ) = sqrt( 15625 ), but I don’t know that value without a calculator.
(A calculator will confirm sqrt ( 15625 ) = 125