Simplify ((a^7)/(2b))^5

${(\frac{a^{7}}{2 b})}^{5}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{a^{7}}{2 b}$ .

$\frac{{(a^{7})}^{5}}{{(2 b)}^{5}}$

Apply the product rule to $2 b$ .

$\frac{{(a^{7})}^{5}}{2^{5} b^{5}}$

Multiply the exponents in ${(a^{7})}^{5}$ .

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

$\frac{a^{7 \cdot 5}}{2^{5} b^{5}}$

Multiply $7$ by $5$ .

$\frac{a^{35}}{2^{5} b^{5}}$

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

$\frac{a^{35}}{32 b^{5}}$