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

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

Simplify the numerator.

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

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

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

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

Multiply the exponents in ${(x^{2})}^{5}$ .

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

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

Multiply $2$ by $5$ .

$\frac{x^{10} {(y^{4})}^{5} z^{5}}{{(x y)}^{2}}$

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

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

$\frac{x^{10} y^{4 \cdot 5} z^{5}}{{(x y)}^{2}}$

Multiply $4$ by $5$ .

$\frac{x^{10} y^{20} z^{5}}{{(x y)}^{2}}$

Reduce the expression by cancelling the common factors.

Apply the product rule to $x y$ .

$\frac{x^{10} y^{20} z^{5}}{x^{2} y^{2}}$

Cancel the common factor of $x^{10}$ and $x^{2}$ .

Factor $x^{2}$ out of $x^{10} y^{20} z^{5}$ .

$\frac{x^{2} (x^{8} y^{20} z^{5})}{x^{2} y^{2}}$

Cancel the common factors.

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

$\frac{x^{2} (x^{8} y^{20} z^{5})}{x^{2} (y^{2})}$

Cancel the common factor.

$\frac{x^{2} (x^{8} y^{20} z^{5})}{x^{2} y^{2}}$

Rewrite the expression.

$\frac{x^{8} y^{20} z^{5}}{y^{2}}$

Cancel the common factor of $y^{20}$ and $y^{2}$ .

Factor $y^{2}$ out of $x^{8} y^{20} z^{5}$ .

$\frac{y^{2} (x^{8} y^{18} z^{5})}{y^{2}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{2} (x^{8} y^{18} z^{5})}{y^{2} \cdot 1}$

Cancel the common factor.

$\frac{y^{2} (x^{8} y^{18} z^{5})}{y^{2} \cdot 1}$

Rewrite the expression.

$\frac{x^{8} y^{18} z^{5}}{1}$

Divide $x^{8} y^{18} z^{5}$ by $1$ .

$x^{8} y^{18} z^{5}$