Evaluate (2^4)/((2^-6)^-1)

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

Step 1

Move ${(2^{- 6})}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$2^{4} \cdot 2^{- 6}$

Step 2

Multiply $2^{4}$ by $2^{- 6}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{4 - 6}$

Subtract $6$ from $4$ .

$2^{- 2}$

Step 3

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

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

Step 4

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

$\frac{1}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$