Simplify ((x^7y^3)/(x^2y))^4

${(\frac{x^{7} y^{3}}{x^{2} y})}^{4}$

Step 1

Cancel the common factor of $x^{7}$ and $x^{2}$ .

Factor $x^{2}$ out of $x^{7} y^{3}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

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

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

Cancel the common factors.

Raise $y$ to the power of $1$ .

${(\frac{y (x^{5} y^{2})}{y^{1}})}^{4}$

Factor $y$ out of $y^{1}$ .

${(\frac{y (x^{5} y^{2})}{y \cdot 1})}^{4}$

Cancel the common factor.

${(\frac{y (x^{5} y^{2})}{y \cdot 1})}^{4}$

Rewrite the expression.

${(\frac{x^{5} y^{2}}{1})}^{4}$

Divide $x^{5} y^{2}$ by $1$ .

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

Step 3

Apply basic rules of exponents.

Apply the product rule to $x^{5} y^{2}$ .

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

Multiply the exponents in ${(x^{5})}^{4}$ .

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

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

Multiply $5$ by $4$ .

$x^{20} {(y^{2})}^{4}$

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

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

$x^{20} y^{2 \cdot 4}$

Multiply $2$ by $4$ .

$x^{20} y^{8}$