Simplify ((8xy^2)/(z^3))^3

${(\frac{8 x y^{2}}{z^{3}})}^{3}$

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

Apply the product rule to $\frac{8 x y^{2}}{z^{3}}$ .

$\frac{{(8 x y^{2})}^{3}}{{(z^{3})}^{3}}$

Apply the product rule to $8 x y^{2}$ .

$\frac{{(8 x)}^{3} {(y^{2})}^{3}}{{(z^{3})}^{3}}$

Apply the product rule to $8 x$ .

$\frac{8^{3} x^{3} {(y^{2})}^{3}}{{(z^{3})}^{3}}$

Simplify the numerator.

Raise $8$ to the power of $3$ .

$\frac{512 x^{3} {(y^{2})}^{3}}{{(z^{3})}^{3}}$

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

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

$\frac{512 x^{3} y^{2 \cdot 3}}{{(z^{3})}^{3}}$

Multiply $2$ by $3$ .

$\frac{512 x^{3} y^{6}}{{(z^{3})}^{3}}$

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

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

$\frac{512 x^{3} y^{6}}{z^{3 \cdot 3}}$

Multiply $3$ by $3$ .

$\frac{512 x^{3} y^{6}}{z^{9}}$