Evaluate 729^(-1/3)

$729^{- \frac{1}{3}}$

Step 1

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

$\frac{1}{729^{\frac{1}{3}}}$

Step 2

Simplify the denominator.

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

$\frac{1}{{(9^{3})}^{\frac{1}{3}}}$

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

$\frac{1}{9^{3 (\frac{1}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1}{9^{3 (\frac{1}{3})}}$

Rewrite the expression.

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

Evaluate the exponent.

$\frac{1}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9}$

Decimal Form:

$0.\overline{1}$