Evaluate ((2xy^5)^3)/(2x^3y^8)

$\frac{{(2 x y^{5})}^{3}}{2 x^{3} y^{8}}$

Simplify the numerator.

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

$\frac{{(2 x)}^{3} {(y^{5})}^{3}}{2 x^{3} y^{8}}$

Apply the product rule to $2 x$ .

$\frac{2^{3} x^{3} {(y^{5})}^{3}}{2 x^{3} y^{8}}$

Raise $2$ to the power of $3$ .

$\frac{8 x^{3} {(y^{5})}^{3}}{2 x^{3} y^{8}}$

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

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

$\frac{8 x^{3} y^{5 \cdot 3}}{2 x^{3} y^{8}}$

Multiply $5$ by $3$ .

$\frac{8 x^{3} y^{15}}{2 x^{3} y^{8}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8 x^{3} y^{15}$ .

$\frac{2 (4 x^{3} y^{15})}{2 x^{3} y^{8}}$

Cancel the common factors.

Factor $2$ out of $2 x^{3} y^{8}$ .

$\frac{2 (4 x^{3} y^{15})}{2 (x^{3} y^{8})}$

Cancel the common factor.

$\frac{2 (4 x^{3} y^{15})}{2 (x^{3} y^{8})}$

Rewrite the expression.

$\frac{4 x^{3} y^{15}}{x^{3} y^{8}}$

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

Cancel the common factor.

$\frac{4 x^{3} y^{15}}{x^{3} y^{8}}$

Rewrite the expression.

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

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

Factor $y^{8}$ out of $4 y^{15}$ .

$\frac{y^{8} (4 y^{7})}{y^{8}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{8} (4 y^{7})}{y^{8} \cdot 1}$

Cancel the common factor.

$\frac{y^{8} (4 y^{7})}{y^{8} \cdot 1}$

Rewrite the expression.

$\frac{4 y^{7}}{1}$

Divide $4 y^{7}$ by $1$ .

$4 y^{7}$