Simplify ((4x^5y)/(16xy^4))^3

${(\frac{4 x^{5} y}{16 x y^{4}})}^{3}$

Step 1

Cancel the common factor of $4$ and $16$ .

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

${(\frac{4 (x^{5} y)}{16 x y^{4}})}^{3}$

Cancel the common factors.

Factor $4$ out of $16 x y^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

Factor $x$ out of $x^{5} y$ .

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

Cancel the common factors.

Factor $x$ out of $4 x y^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

Factor $y$ out of $x^{4} y$ .

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

Cancel the common factors.

Factor $y$ out of $4 y^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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

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

Apply the product rule to $4 y^{3}$ .

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

Step 5

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

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

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

Multiply $4$ by $3$ .

$\frac{x^{12}}{4^{3} {(y^{3})}^{3}}$

Step 6

Simplify the denominator.

Raise $4$ to the power of $3$ .

$\frac{x^{12}}{64 {(y^{3})}^{3}}$

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

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

$\frac{x^{12}}{64 y^{3 \cdot 3}}$

Multiply $3$ by $3$ .

$\frac{x^{12}}{64 y^{9}}$

Simplify ((4x^5y)/(16xy^4))^3

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