Simplify ((2x^3y^11zw^6)/(3xy^7z^4w^5))^3

${(\frac{2 x^{3} y^{11} z w^{6}}{3 x y^{7} z^{4} w^{5}})}^{3}$

Cancel the common factor of $x^{3}$ and $x$ .

Factor $x$ out of $2 x^{3} y^{11} z w^{6}$ .

${(\frac{x (2 x^{2} y^{11} z w^{6})}{3 x y^{7} z^{4} w^{5}})}^{3}$

Cancel the common factors.

Factor $x$ out of $3 x y^{7} z^{4} w^{5}$ .

${(\frac{x (2 x^{2} y^{11} z w^{6})}{x (3 y^{7} z^{4} w^{5})})}^{3}$

Cancel the common factor.

${(\frac{x (2 x^{2} y^{11} z w^{6})}{x (3 y^{7} z^{4} w^{5})})}^{3}$

Rewrite the expression.

${(\frac{2 x^{2} y^{11} z w^{6}}{3 y^{7} z^{4} w^{5}})}^{3}$

Cancel the common factor of $y^{11}$ and $y^{7}$ .

Factor $y^{7}$ out of $2 x^{2} y^{11} z w^{6}$ .

${(\frac{y^{7} (2 x^{2} y^{4} z w^{6})}{3 y^{7} z^{4} w^{5}})}^{3}$

Cancel the common factors.

Factor $y^{7}$ out of $3 y^{7} z^{4} w^{5}$ .

${(\frac{y^{7} (2 x^{2} y^{4} z w^{6})}{y^{7} (3 z^{4} w^{5})})}^{3}$

Cancel the common factor.

${(\frac{y^{7} (2 x^{2} y^{4} z w^{6})}{y^{7} (3 z^{4} w^{5})})}^{3}$

Rewrite the expression.

${(\frac{2 x^{2} y^{4} z w^{6}}{3 z^{4} w^{5}})}^{3}$

Cancel the common factor of $z$ and $z^{4}$ .

Factor $z$ out of $2 x^{2} y^{4} z w^{6}$ .

${(\frac{z (2 x^{2} y^{4} w^{6})}{3 z^{4} w^{5}})}^{3}$

Cancel the common factors.

Factor $z$ out of $3 z^{4} w^{5}$ .

${(\frac{z (2 x^{2} y^{4} w^{6})}{z (3 z^{3} w^{5})})}^{3}$

Cancel the common factor.

${(\frac{z (2 x^{2} y^{4} w^{6})}{z (3 z^{3} w^{5})})}^{3}$

Rewrite the expression.

${(\frac{2 x^{2} y^{4} w^{6}}{3 z^{3} w^{5}})}^{3}$

Cancel the common factor of $w^{6}$ and $w^{5}$ .

Factor $w^{5}$ out of $2 x^{2} y^{4} w^{6}$ .

${(\frac{w^{5} (2 x^{2} y^{4} w)}{3 z^{3} w^{5}})}^{3}$

Cancel the common factors.

Factor $w^{5}$ out of $3 z^{3} w^{5}$ .

${(\frac{w^{5} (2 x^{2} y^{4} w)}{w^{5} (3 z^{3})})}^{3}$

Cancel the common factor.

${(\frac{w^{5} (2 x^{2} y^{4} w)}{w^{5} (3 z^{3})})}^{3}$

Rewrite the expression.

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

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

Apply the product rule to $\frac{2 x^{2} y^{4} w}{3 z^{3}}$ .

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

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

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

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

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

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

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

Apply the product rule to $3 z^{3}$ .

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

Simplify the numerator.

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

$\frac{8 {(x^{2})}^{3} {(y^{4})}^{3} w^{3}}{3^{3} {(z^{3})}^{3}}$

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

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

$\frac{8 x^{2 \cdot 3} {(y^{4})}^{3} w^{3}}{3^{3} {(z^{3})}^{3}}$

Multiply $2$ by $3$ .

$\frac{8 x^{6} {(y^{4})}^{3} w^{3}}{3^{3} {(z^{3})}^{3}}$

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

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

$\frac{8 x^{6} y^{4 \cdot 3} w^{3}}{3^{3} {(z^{3})}^{3}}$

Multiply $4$ by $3$ .

$\frac{8 x^{6} y^{12} w^{3}}{3^{3} {(z^{3})}^{3}}$

Simplify the denominator.

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

$\frac{8 x^{6} y^{12} w^{3}}{27 {(z^{3})}^{3}}$

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

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

$\frac{8 x^{6} y^{12} w^{3}}{27 z^{3 \cdot 3}}$

Multiply $3$ by $3$ .

$\frac{8 x^{6} y^{12} w^{3}}{27 z^{9}}$

Simplify ((2x^3y^11zw^6)/(3xy^7z^4w^5))^3

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