Simplify ((a^2)/(2^b))^4

${(\frac{a^{2}}{2^{b}})}^{4}$

Apply the product rule to $\frac{a^{2}}{2^{b}}$ .

$\frac{{(a^{2})}^{4}}{{(2^{b})}^{4}}$

Multiply the exponents in ${(a^{2})}^{4}$ .

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

$\frac{a^{2 \cdot 4}}{{(2^{b})}^{4}}$

Multiply $2$ by $4$ .

$\frac{a^{8}}{{(2^{b})}^{4}}$

Multiply the exponents in ${(2^{b})}^{4}$ .

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

$\frac{a^{8}}{2^{b \cdot 4}}$

Move $4$ to the left of $b$ .

$\frac{a^{8}}{2^{4 b}}$