Simplify ( cube root of 729)^-2

${(\sqrt[3]{729})}^{- 2}$

Step 1

Rewrite $729$ as $9^{3}$ .

${\sqrt[3]{9^{3}}}^{- 2}$

Step 2

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

$9^{- 2}$

Step 3

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

$\frac{1}{9^{2}}$

Step 4

Raise $9$ to the power of $2$ .

$\frac{1}{81}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{81}$

Decimal Form:

$0.01234567 \dots$