Simplify ((5x^3y)/(20xy^5))^4

${(\frac{5 x^{3} y}{20 x y^{5}})}^{4}$

Step 1

Cancel the common factor of $5$ and $20$ .

Factor $5$ out of $5 x^{3} y$ .

${(\frac{5 (x^{3} y)}{20 x y^{5}})}^{4}$

Cancel the common factors.

Factor $5$ out of $20 x y^{5}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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

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

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

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

Step 5

Multiply the exponents in ${(x^{2})}^{4}$ .

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

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

Multiply $2$ by $4$ .

$\frac{x^{8}}{4^{4} {(y^{4})}^{4}}$

Step 6

Simplify the denominator.

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

$\frac{x^{8}}{256 {(y^{4})}^{4}}$

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

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

$\frac{x^{8}}{256 y^{4 \cdot 4}}$

Multiply $4$ by $4$ .

$\frac{x^{8}}{256 y^{16}}$

Simplify ((5x^3y)/(20xy^5))^4

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