Simplify (8^2)/(2^-3)

$\frac{8^{2}}{2^{- 3}}$

Step 1

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

$8^{2} \cdot 2^{3}$

Step 2

Rewrite $8$ as $2^{3}$ .

${(2^{3})}^{2} \cdot 2^{3}$

Step 3

Multiply the exponents in ${(2^{3})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $3$ by $2$ .

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

Step 4

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

$2^{6 + 3}$

Step 5

Add $6$ and $3$ .

$2^{9}$

Step 6

Raise $2$ to the power of $9$ .

$512$