Basic Math Examples

$\frac{2^{- 3} + 3^{- 2}}{2^{- 4} + 3^{- 1}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{\frac{1}{2^{3}} + 3^{- 2}}{2^{- 4} + 3^{- 1}}$

Step 1.2

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

$\frac{\frac{1}{8} + 3^{- 2}}{2^{- 4} + 3^{- 1}}$

Step 1.3

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

$\frac{\frac{1}{8} + \frac{1}{3^{2}}}{2^{- 4} + 3^{- 1}}$

Step 1.4

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

$\frac{\frac{1}{8} + \frac{1}{9}}{2^{- 4} + 3^{- 1}}$

Step 1.5

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

$\frac{\frac{1}{8} \cdot \frac{9}{9} + \frac{1}{9}}{2^{- 4} + 3^{- 1}}$

Step 1.6

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

$\frac{\frac{1}{8} \cdot \frac{9}{9} + \frac{1}{9} \cdot \frac{8}{8}}{2^{- 4} + 3^{- 1}}$

Step 1.7

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

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Step 1.7.1

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

$\frac{\frac{9}{8 \cdot 9} + \frac{1}{9} \cdot \frac{8}{8}}{2^{- 4} + 3^{- 1}}$

Step 1.7.2

Multiply $8$ by $9$ .

$\frac{\frac{9}{72} + \frac{1}{9} \cdot \frac{8}{8}}{2^{- 4} + 3^{- 1}}$

Step 1.7.3

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

$\frac{\frac{9}{72} + \frac{8}{9 \cdot 8}}{2^{- 4} + 3^{- 1}}$

Step 1.7.4

Multiply $9$ by $8$ .

$\frac{\frac{9}{72} + \frac{8}{72}}{2^{- 4} + 3^{- 1}}$

Step 1.8

Combine the numerators over the common denominator.

$\frac{\frac{9 + 8}{72}}{2^{- 4} + 3^{- 1}}$

Step 1.9

Add $9$ and $8$ .

$\frac{\frac{17}{72}}{2^{- 4} + 3^{- 1}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{\frac{17}{72}}{\frac{1}{2^{4}} + 3^{- 1}}$

Step 2.2

Raise $2$ to the power of $4$ .

$\frac{\frac{17}{72}}{\frac{1}{16} + 3^{- 1}}$

Step 2.3

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

$\frac{\frac{17}{72}}{\frac{1}{16} + \frac{1}{3}}$

Step 2.4

To write $\frac{1}{16}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{17}{72}}{\frac{1}{16} \cdot \frac{3}{3} + \frac{1}{3}}$

Step 2.5

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\frac{\frac{17}{72}}{\frac{1}{16} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{16}{16}}$

Step 2.6

Write each expression with a common denominator of $48$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.6.1

Multiply $\frac{1}{16}$ by $\frac{3}{3}$ .

$\frac{\frac{17}{72}}{\frac{3}{16 \cdot 3} + \frac{1}{3} \cdot \frac{16}{16}}$

Step 2.6.2

Multiply $16$ by $3$ .

$\frac{\frac{17}{72}}{\frac{3}{48} + \frac{1}{3} \cdot \frac{16}{16}}$

Step 2.6.3

Multiply $\frac{1}{3}$ by $\frac{16}{16}$ .

$\frac{\frac{17}{72}}{\frac{3}{48} + \frac{16}{3 \cdot 16}}$

Step 2.6.4

Multiply $3$ by $16$ .

$\frac{\frac{17}{72}}{\frac{3}{48} + \frac{16}{48}}$

Step 2.7

Combine the numerators over the common denominator.

$\frac{\frac{17}{72}}{\frac{3 + 16}{48}}$

Step 2.8

Add $3$ and $16$ .

$\frac{\frac{17}{72}}{\frac{19}{48}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{17}{72} \cdot \frac{48}{19}$

Step 4

Cancel the common factor of $24$ .

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Step 4.1

Factor $24$ out of $72$ .

$\frac{17}{24 (3)} \cdot \frac{48}{19}$

Step 4.2

Factor $24$ out of $48$ .

$\frac{17}{24 \cdot 3} \cdot \frac{24 \cdot 2}{19}$

Step 4.3

Cancel the common factor.

$\frac{17}{24 \cdot 3} \cdot \frac{24 \cdot 2}{19}$

Step 4.4

Rewrite the expression.

$\frac{17}{3} \cdot \frac{2}{19}$

Step 5

Multiply $\frac{17}{3}$ by $\frac{2}{19}$ .

$\frac{17 \cdot 2}{3 \cdot 19}$

Step 6

Multiply.

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Step 6.1

Multiply $17$ by $2$ .

$\frac{34}{3 \cdot 19}$

Step 6.2

Multiply $3$ by $19$ .

$\frac{34}{57}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{34}{57}$

Decimal Form:

$0.59649122 \dots$