Evaluate ((4r^2)/(3s^5))^3

${(\frac{4 r^{2}}{3 s^{5}})}^{3}$

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

Apply the product rule to $\frac{4 r^{2}}{3 s^{5}}$ .

$\frac{{(4 r^{2})}^{3}}{{(3 s^{5})}^{3}}$

Apply the product rule to $4 r^{2}$ .

$\frac{4^{3} {(r^{2})}^{3}}{{(3 s^{5})}^{3}}$

Apply the product rule to $3 s^{5}$ .

$\frac{4^{3} {(r^{2})}^{3}}{3^{3} {(s^{5})}^{3}}$

Simplify the numerator.

Raise $4$ to the power of $3$ .

$\frac{64 {(r^{2})}^{3}}{3^{3} {(s^{5})}^{3}}$

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

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

$\frac{64 r^{2 \cdot 3}}{3^{3} {(s^{5})}^{3}}$

Multiply $2$ by $3$ .

$\frac{64 r^{6}}{3^{3} {(s^{5})}^{3}}$

Simplify the denominator.

Raise $3$ to the power of $3$ .

$\frac{64 r^{6}}{27 {(s^{5})}^{3}}$

Multiply the exponents in ${(s^{5})}^{3}$ .

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

$\frac{64 r^{6}}{27 s^{5 \cdot 3}}$

Multiply $5$ by $3$ .

$\frac{64 r^{6}}{27 s^{15}}$