# How do you simplify 25^(3/2)?

Feb 3, 2015

The number reads as 25 to the power of (3/2), which simplifies to $\sqrt{15625}$.

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 ${25}^{3}$.
${25}^{\frac{3}{2}}$
$= \sqrt{{25}^{3}}$

Then simplify and solve.
$= \sqrt{25 \cdot 25 \cdot 25}$
$= \sqrt{15625}$
$= 160.0781059$