What is the correct simplification of 25^3/2

Answer 1

To simplify \( 25^{3/2} \), you can proceed as follows:

1. Rewrite \( 25 \) as \( 5^2 \): \[ 25^{3/2} = (5^2)^{3/2} \]

2. Apply the power of a power property, which states that \( (a^m)^n = a^{m \cdot n} \): \[ (5^2)^{3/2} = 5^{2 \cdot \frac{3}{2}} = 5^3 \]

3. Now calculate \( 5^3 \): \[ 5^3 = 125 \]

Thus, the simplified form of \( 25^{3/2} \) is \( \boxed{125} \).