Evaluate (1/25)^(-3/2)

${(\frac{1}{25})}^{- \frac{3}{2}}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

$25^{\frac{3}{2}}$

Step 2

Simplify the expression.

Rewrite $25$ as $5^{2}$ .

${(5^{2})}^{\frac{3}{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$5^{2 (\frac{3}{2})}$

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

$5^{2 (\frac{3}{2})}$

Rewrite the expression.

$5^{3}$

Step 4

Raise $5$ to the power of $3$ .

$125$