Evaluate (1/3)^2+(9/10)^-1

${(\frac{1}{3})}^{2} + {(\frac{9}{10})}^{- 1}$

Step 1

Simplify each term.

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

$\frac{1^{2}}{3^{2}} + {(\frac{9}{10})}^{- 1}$

One to any power is one.

$\frac{1}{3^{2}} + {(\frac{9}{10})}^{- 1}$

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

$\frac{1}{9} + {(\frac{9}{10})}^{- 1}$

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

$\frac{1}{9} + \frac{10}{9}$

Step 2

Combine fractions.

Combine the numerators over the common denominator.

$\frac{1 + 10}{9}$

Add $1$ and $10$ .

$\frac{11}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{9}$

Decimal Form:

$1.\overline{2}$

Mixed Number Form:

$1 \frac{2}{9}$