Let's solve the expression [tex]\( 25^{\frac{3}{2}} \)[/tex] step by step.
1. Understanding the exponent [tex]\(\frac{3}{2}\)[/tex]:
- The exponent can be broken down into two parts:
- [tex]\( \frac{3}{2} = 1.5 = 1 + 0.5 = 1 + \frac{1}{2} \)[/tex].
- Alternatively, it can also be viewed as [tex]\( \left(25^{\frac{1}{2}}\right)^3 \)[/tex].
2. Calculating the square root:
- First, we take the square root of 25. Recall that the square root of a number [tex]\( x \)[/tex] is a number [tex]\( y \)[/tex] such that [tex]\( y^2 = x \)[/tex].
[tex]\[
\sqrt{25} = 5
\][/tex]
3. Raising the result to the power of 3:
- Now, we raise the result (which is 5) to the power of 3.
[tex]\[
5^3 = 5 \times 5 \times 5 = 125
\][/tex]
Therefore, the simplified form of [tex]\( 25^{\frac{3}{2}} \)[/tex] is [tex]\( 125 \)[/tex].
Thus, the correct answer is:
[tex]\[
125
\][/tex]
