To simplify \( 25^{3/2} \):
- First, recognize that \( 25^{3/2} \) can be rewritten as \( (25^{1/2})^3 \).
- Calculate \( 25^{1/2} \), which is the square root of \( 25 \). The square root of \( 25 \) is \( 5 \).
- Now, raise \( 5 \) to the power of \( 3 \): \[ 5^3 = 125. \]
Thus, the correct simplification of \( 25^{3/2} \) is \( 125 \). None of the provided options (37.5, 37.56, 256, 251, 251, 575) are correct. The answer should be \( 125 \).