Simplify ((3x)/(zy^2))^6

${(\frac{3 x}{z y^{2}})}^{6}$

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

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

$\frac{{(3 x)}^{6}}{{(z y^{2})}^{6}}$

Apply the product rule to $3 x$ .

$\frac{3^{6} x^{6}}{{(z y^{2})}^{6}}$

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

$\frac{3^{6} x^{6}}{z^{6} {(y^{2})}^{6}}$

Raise $3$ to the power of $6$ .

$\frac{729 x^{6}}{z^{6} {(y^{2})}^{6}}$

Multiply the exponents in ${(y^{2})}^{6}$ .

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

$\frac{729 x^{6}}{z^{6} y^{2 \cdot 6}}$

Multiply $2$ by $6$ .

$\frac{729 x^{6}}{z^{6} y^{12}}$