Simplify ((3x^2y^6)/(6xy^2))^3

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

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3 x^{2} y^{6}$ .

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

Cancel the common factors.

Factor $3$ out of $6 x y^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x^{2}$ and $x$ .

Factor $x$ out of $x^{2} y^{6}$ .

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

Cancel the common factors.

Factor $x$ out of $2 x y^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y^{6}$ and $y^{2}$ .

Factor $y^{2}$ out of $x y^{6}$ .

${(\frac{y^{2} (x y^{4})}{2 y^{2}})}^{3}$

Cancel the common factors.

Factor $y^{2}$ out of $2 y^{2}$ .

${(\frac{y^{2} (x y^{4})}{y^{2} \cdot 2})}^{3}$

Cancel the common factor.

${(\frac{y^{2} (x y^{4})}{y^{2} \cdot 2})}^{3}$

Rewrite the expression.

${(\frac{x y^{4}}{2})}^{3}$

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

Apply the product rule to $\frac{x y^{4}}{2}$ .

$\frac{{(x y^{4})}^{3}}{2^{3}}$

Apply the product rule to $x y^{4}$ .

$\frac{x^{3} {(y^{4})}^{3}}{2^{3}}$

Multiply the exponents in ${(y^{4})}^{3}$ .

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

$\frac{x^{3} y^{4 \cdot 3}}{2^{3}}$

Multiply $4$ by $3$ .

$\frac{x^{3} y^{12}}{2^{3}}$

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

$\frac{x^{3} y^{12}}{8}$