Simplify (8x^2y)/((4xy)^2)

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

Simplify the denominator.

Apply the product rule to $4 x y$ .

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

Apply the product rule to $4 x$ .

$\frac{8 x^{2} y}{4^{2} x^{2} y^{2}}$

Raise $4$ to the power of $2$ .

$\frac{8 x^{2} y}{16 x^{2} y^{2}}$

$\frac{8 x^{2} y}{16 x^{2} y^{2}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $8$ and $16$ .

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

$\frac{8 (x^{2} y)}{16 x^{2} y^{2}}$

Cancel the common factors.

Factor $8$ out of $16 x^{2} y^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{y}{2 y^{2}}$

$\frac{y}{2 y^{2}}$

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

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

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

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

$\frac{y \cdot 1}{2 y^{2}}$

Cancel the common factors.

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

$\frac{y \cdot 1}{y (2 y)}$

Cancel the common factor.

$\frac{y \cdot 1}{y (2 y)}$

Rewrite the expression.

$\frac{1}{2 y}$

$\frac{1}{2 y}$

$\frac{1}{2 y}$

$\frac{1}{2 y}$

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