Find the Product (4xy^3)/(x^2y)*y/(8x)

$\frac{4 x y^{3}}{x^{2} y} \cdot \frac{y}{8 x}$

Combine.

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

Multiply $y^{3}$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y^{3}$ .

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

$\frac{4 x (y^{1} y^{3})}{x^{2} y (8 x)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 x y^{1 + 3}}{x^{2} y (8 x)}$

$\frac{4 x y^{1 + 3}}{x^{2} y (8 x)}$

Add $1$ and $3$ .

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

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

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{2}$ .

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

$\frac{4 x y^{4}}{x^{1} x^{2} y \cdot 8}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 x y^{4}}{x^{1 + 2} y \cdot 8}$

$\frac{4 x y^{4}}{x^{1 + 2} y \cdot 8}$

Add $1$ and $2$ .

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

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

Cancel the common factor of $4$ and $8$ .

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

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

Cancel the common factors.

Factor $4$ out of $x^{3} y \cdot 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Move $2$ to the left of $x^{2}$ .

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

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