Evaluate (1/16)^(-5/4)

${(\frac{1}{16})}^{- \frac{5}{4}}$

Step 1

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

$16^{\frac{5}{4}}$

Step 2

Simplify the expression.

Rewrite $16$ as $2^{4}$ .

${(2^{4})}^{\frac{5}{4}}$

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

$2^{4 (\frac{5}{4})}$

Step 3

Cancel the common factor of $4$ .

Cancel the common factor.

$2^{4 (\frac{5}{4})}$

Rewrite the expression.

$2^{5}$

Step 4

Raise $2$ to the power of $5$ .

$32$