Evaluate (5/9)^-3

${(\frac{5}{9})}^{- 3}$

Step 1

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

${(\frac{9}{5})}^{3}$

Step 2

Apply the product rule to $\frac{9}{5}$ .

$\frac{9^{3}}{5^{3}}$

Step 3

Raise $9$ to the power of $3$ .

$\frac{729}{5^{3}}$

Step 4

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

$\frac{729}{125}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{729}{125}$

Decimal Form:

$5.832$

Mixed Number Form:

$5 \frac{104}{125}$