Simplify (2^-3+3^-2)/(2^-2)

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

Step 1

Move $2^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$(2^{- 3} + 3^{- 2}) \cdot 2^{2}$

Step 2

Simplify each term.

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

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

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

$(\frac{1}{8} + 3^{- 2}) \cdot 2^{2}$

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

$(\frac{1}{8} + \frac{1}{3^{2}}) \cdot 2^{2}$

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

$(\frac{1}{8} + \frac{1}{9}) \cdot 2^{2}$

Step 3

To write $\frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$(\frac{1}{8} \cdot \frac{9}{9} + \frac{1}{9}) \cdot 2^{2}$

Step 4

To write $\frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$(\frac{1}{8} \cdot \frac{9}{9} + \frac{1}{9} \cdot \frac{8}{8}) \cdot 2^{2}$

Step 5

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{8}$ by $\frac{9}{9}$ .

$(\frac{9}{8 \cdot 9} + \frac{1}{9} \cdot \frac{8}{8}) \cdot 2^{2}$

Multiply $8$ by $9$ .

$(\frac{9}{72} + \frac{1}{9} \cdot \frac{8}{8}) \cdot 2^{2}$

Multiply $\frac{1}{9}$ by $\frac{8}{8}$ .

$(\frac{9}{72} + \frac{8}{9 \cdot 8}) \cdot 2^{2}$

Multiply $9$ by $8$ .

$(\frac{9}{72} + \frac{8}{72}) \cdot 2^{2}$

Step 6

Simplify the expression.

Combine the numerators over the common denominator.

$\frac{9 + 8}{72} \cdot 2^{2}$

Add $9$ and $8$ .

$\frac{17}{72} \cdot 2^{2}$

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

$\frac{17}{72} \cdot 4$

Step 7

Cancel the common factor of $4$ .

Factor $4$ out of $72$ .

$\frac{17}{4 (18)} \cdot 4$

Cancel the common factor.

$\frac{17}{4 \cdot 18} \cdot 4$

Rewrite the expression.

$\frac{17}{18}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{18}$

Decimal Form:

$0.9\overline{4}$

Simplify (2^-3+3^-2)/(2^-2)

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