Evaluate 7^-1+9^-1

$7^{- 1} + 9^{- 1}$

Step 1

Simplify each term.

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{7} + 9^{- 1}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{7} + \frac{1}{9}$

Step 2

To write $\frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{1}{7} \cdot \frac{9}{9} + \frac{1}{9}$

Step 3

To write $\frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{1}{7} \cdot \frac{9}{9} + \frac{1}{9} \cdot \frac{7}{7}$

Step 4

Write each expression with a common denominator of $63$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{7}$ by $\frac{9}{9}$ .

$\frac{9}{7 \cdot 9} + \frac{1}{9} \cdot \frac{7}{7}$

Multiply $7$ by $9$ .

$\frac{9}{63} + \frac{1}{9} \cdot \frac{7}{7}$

Multiply $\frac{1}{9}$ by $\frac{7}{7}$ .

$\frac{9}{63} + \frac{7}{9 \cdot 7}$

Multiply $9$ by $7$ .

$\frac{9}{63} + \frac{7}{63}$

Step 5

Combine the numerators over the common denominator.

$\frac{9 + 7}{63}$

Step 6

Add $9$ and $7$ .

$\frac{16}{63}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{63}$

Decimal Form:

$0.\overline{253968}$