Simplify (2^-3)/(2^-2)*2^6

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

Step 1

Simplify the numerator.

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

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

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

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

Step 2

Simplify the denominator.

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

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

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 $4$ .

Factor $4$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Cancel the common factor of $2$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

$2^{5}$

Step 6

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

$32$