To simplify the given expression [tex]\(25^{\frac{3}{2}}\)[/tex], we can break down the exponent into more manageable components using properties of exponents and roots.
1. Understand the exponent: The exponent [tex]\(\frac{3}{2}\)[/tex] can be interpreted in parts:
[tex]\[
25^{\frac{3}{2}} = 25^{1 + \frac{1}{2}} = 25^1 \cdot 25^{\frac{1}{2}}
\][/tex]
2. Simplify the base powers:
[tex]\[
25^1 = 25
\][/tex]
and
[tex]\[
25^{\frac{1}{2}} \text{ is the same as } \sqrt{25} = 5
\][/tex]
3. Combine the simplified parts:
[tex]\[
25^{\frac{3}{2}} = 25 \cdot 5 = 125
\][/tex]
So, the correct simplification of [tex]\(25^{\frac{3}{2}}\)[/tex] is [tex]\(125\)[/tex].
Therefore, among the given options, the correct answer is:
[tex]\[
\boxed{125}
\][/tex]
