Evaluate ( fourth root of 16)^-7

${(\sqrt[4]{16})}^{- 7}$

Step 1

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

${\sqrt[4]{2^{4}}}^{- 7}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$2^{- 7}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{2^{7}}$

Step 4

Raise $2$ to the power of $7$ .

$\frac{1}{128}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{128}$

Decimal Form:

$0.0078125$