Simplify ((x^2y^5)^3)/((xy^2)^4)

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

Simplify the numerator.

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

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

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

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

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

Multiply $2$ by $3$ .

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

Multiply the exponents in ${(y^{5})}^{3}$ .

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

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

Multiply $5$ by $3$ .

$\frac{x^{6} y^{15}}{{(x y^{2})}^{4}}$

Simplify the denominator.

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

$\frac{x^{6} y^{15}}{x^{4} {(y^{2})}^{4}}$

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

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

$\frac{x^{6} y^{15}}{x^{4} y^{2 \cdot 4}}$

Multiply $2$ by $4$ .

$\frac{x^{6} y^{15}}{x^{4} y^{8}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x^{6}$ and $x^{4}$ .

Factor $x^{4}$ out of $x^{6} y^{15}$ .

$\frac{x^{4} (x^{2} y^{15})}{x^{4} y^{8}}$

Cancel the common factors.

Factor $x^{4}$ out of $x^{4} y^{8}$ .

$\frac{x^{4} (x^{2} y^{15})}{x^{4} (y^{8})}$

Cancel the common factor.

$\frac{x^{4} (x^{2} y^{15})}{x^{4} y^{8}}$

Rewrite the expression.

$\frac{x^{2} y^{15}}{y^{8}}$

Cancel the common factor of $y^{15}$ and $y^{8}$ .

Factor $y^{8}$ out of $x^{2} y^{15}$ .

$\frac{y^{8} (x^{2} y^{7})}{y^{8}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{8} (x^{2} y^{7})}{y^{8} \cdot 1}$

Cancel the common factor.

$\frac{y^{8} (x^{2} y^{7})}{y^{8} \cdot 1}$

Rewrite the expression.

$\frac{x^{2} y^{7}}{1}$

Divide $x^{2} y^{7}$ by $1$ .

$x^{2} y^{7}$