Simplify (3xy^3)/(x^3y)*y/(6x)

$\frac{3 x y^{3}}{x^{3} y} \cdot \frac{y}{6 x}$

Step 1

Combine.

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

Step 2

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

Move $y$ .

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

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

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

$\frac{3 x (y^{1} y^{3})}{x^{3} y (6 x)}$

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

$\frac{3 x y^{1 + 3}}{x^{3} y (6 x)}$

$\frac{3 x y^{1 + 3}}{x^{3} y (6 x)}$

Add $1$ and $3$ .

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

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

Step 3

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

Move $x$ .

$\frac{3 x y^{4}}{x \cdot x^{3} y \cdot 6}$

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

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

$\frac{3 x y^{4}}{x^{1} x^{3} y \cdot 6}$

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

$\frac{3 x y^{4}}{x^{1 + 3} y \cdot 6}$

$\frac{3 x y^{4}}{x^{1 + 3} y \cdot 6}$

Add $1$ and $3$ .

$\frac{3 x y^{4}}{x^{4} y \cdot 6}$

$\frac{3 x y^{4}}{x^{4} y \cdot 6}$

Step 4

Cancel the common factor of $3$ and $6$ .

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

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

Cancel the common factors.

Factor $3$ out of $x^{4} y \cdot 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 5

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

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

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

Cancel the common factors.

Factor $x$ out of $x^{4} y \cdot 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 6

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 7

Move $2$ to the left of $x^{3}$ .

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

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