Find the Exact Value (1/3)^2+3^2

${(\frac{1}{3})}^{2} + 3^{2}$

Simplify each term.

Apply the product rule to $\frac{1}{3}$ .

$\frac{1^{2}}{3^{2}} + 3^{2}$

One to any power is one.

$\frac{1}{3^{2}} + 3^{2}$

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

$\frac{1}{9} + 3^{2}$

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

$\frac{1}{9} + 9$

To write $9$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{1}{9} + 9 \cdot \frac{9}{9}$

Combine $9$ and $\frac{9}{9}$ .

$\frac{1}{9} + \frac{9 \cdot 9}{9}$

Combine the numerators over the common denominator.

$\frac{1 + 9 \cdot 9}{9}$

Simplify the numerator.

Multiply $9$ by $9$ .

$\frac{1 + 81}{9}$

Add $1$ and $81$ .

$\frac{82}{9}$

The result can be shown in multiple forms.

Exact Form:

$\frac{82}{9}$

Decimal Form:

$9.\overline{1}$

Mixed Number Form:

$9 \frac{1}{9}$