Evaluate (5/9)^-2

${(\frac{5}{9})}^{- 2}$

Step 1

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

${(\frac{9}{5})}^{2}$

Step 2

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

$\frac{9^{2}}{5^{2}}$

Step 3

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

$\frac{81}{5^{2}}$

Step 4

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

$\frac{81}{25}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{25}$

Decimal Form:

$3.24$

Mixed Number Form:

$3 \frac{6}{25}$