Evaluate (4/9)^-2

${(\frac{4}{9})}^{- 2}$

Step 1

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

${(\frac{9}{4})}^{2}$

Step 2

Apply the product rule to $\frac{9}{4}$ .

$\frac{9^{2}}{4^{2}}$

Step 3

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

$\frac{81}{4^{2}}$

Step 4

Raise $4$ to the power of $2$ .

$\frac{81}{16}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{16}$

Decimal Form:

$5.0625$

Mixed Number Form:

$5 \frac{1}{16}$