Find the Exact Value 2/(2^-3)

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

Step 1

Move $2^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$2 \cdot 2^{3}$

Step 2

Multiply $2$ by $2^{3}$ by adding the exponents.

Multiply $2$ by $2^{3}$ .

Raise $2$ to the power of $1$ .

$2^{1} \cdot 2^{3}$

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

$2^{1 + 3}$

Add $1$ and $3$ .

$2^{4}$

Step 3

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

$16$