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

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

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

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

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

Apply the product rule to $3 x y^{3}$ .

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

Apply the product rule to $3 x$ .

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

Apply the product rule to $2 z$ .

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

Simplify the numerator.

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

$\frac{27 x^{3} {(y^{3})}^{3}}{2^{3} z^{3}}$

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

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

$\frac{27 x^{3} y^{3 \cdot 3}}{2^{3} z^{3}}$

Multiply $3$ by $3$ .

$\frac{27 x^{3} y^{9}}{2^{3} z^{3}}$

Raise $2$ to the power of $3$ .

$\frac{27 x^{3} y^{9}}{8 z^{3}}$