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

May 26, 2016

I found $0.008$

#### Explanation:

We first get rid of the minus sign by writing:
${25}^{- \frac{3}{2}} = \frac{1}{25} ^ \left(\frac{3}{2}\right)$
A fractional exponent correspond to a root as:
${x}^{\frac{m}{n}} = \sqrt[n]{{x}^{m}}$
so we get:
$\frac{1}{25} ^ \left(\frac{3}{2}\right) = \frac{1}{\sqrt{{25}^{3}}} = \frac{1}{\sqrt{{25}^{2} \cdot 25}} = \frac{1}{25 \cdot 5} = 0.008$