Find the Exact Value (3/5)^-2

${(\frac{3}{5})}^{- 2}$

Step 1

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

${(\frac{5}{3})}^{2}$

Step 2

Apply the product rule to $\frac{5}{3}$ .

$\frac{5^{2}}{3^{2}}$

Step 3

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

$\frac{25}{3^{2}}$

Step 4

Raise $3$ to the power of $2$ .

$\frac{25}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{9}$

Decimal Form:

$2.\overline{7}$

Mixed Number Form:

$2 \frac{7}{9}$