Algebra Examples

$\frac{2^{- 3}}{2^{- 2}} \cdot 2^{6}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{\frac{1}{2^{3}}}{2^{- 2}} \cdot 2^{6}$

Step 1.2

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

$\frac{\frac{1}{8}}{2^{- 2}} \cdot 2^{6}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{\frac{1}{8}}{\frac{1}{2^{2}}} \cdot 2^{6}$

Step 2.2

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

$\frac{\frac{1}{8}}{\frac{1}{4}} \cdot 2^{6}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{8} \cdot 4 \cdot 2^{6}$

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Factor $4$ out of $8$ .

$\frac{1}{4 (2)} \cdot 4 \cdot 2^{6}$

Step 4.2

Cancel the common factor.

$\frac{1}{4 \cdot 2} \cdot 4 \cdot 2^{6}$

Step 4.3

Rewrite the expression.

$\frac{1}{2} \cdot 2^{6}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $2^{6}$ .

$\frac{1}{2} \cdot (2 \cdot 2^{5})$

Step 5.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 2^{5})$

Step 5.3

Rewrite the expression.

$2^{5}$

Step 6

Raise $2$ to the power of $5$ .

$32$