Simplify (6x^3y)/(y^2)*(x^2y^4)/(3xy)

$\frac{6 x^{3} y}{y^{2}} \cdot \frac{x^{2} y^{4}}{3 x y}$

Step 1

Combine.

$\frac{6 x^{3} y (x^{2} y^{4})}{y^{2} (3 x y)}$

Step 2

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{6 (x^{2} x^{3}) y \cdot y^{4}}{y^{2} (3 x y)}$

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

$\frac{6 x^{2 + 3} y \cdot y^{4}}{y^{2} (3 x y)}$

Add $2$ and $3$ .

$\frac{6 x^{5} y \cdot y^{4}}{y^{2} (3 x y)}$

Step 3

Multiply $y$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$\frac{6 x^{5} (y^{4} y)}{y^{2} (3 x y)}$

Multiply $y^{4}$ by $y$ .

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

$\frac{6 x^{5} (y^{4} y^{1})}{y^{2} (3 x y)}$

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

$\frac{6 x^{5} y^{4 + 1}}{y^{2} (3 x y)}$

Add $4$ and $1$ .

$\frac{6 x^{5} y^{5}}{y^{2} (3 x y)}$

Step 4

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

Move $y$ .

$\frac{6 x^{5} y^{5}}{y \cdot y^{2} (3 x)}$

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

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

$\frac{6 x^{5} y^{5}}{y^{1} y^{2} (3 x)}$

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

$\frac{6 x^{5} y^{5}}{y^{1 + 2} (3 x)}$

Add $1$ and $2$ .

$\frac{6 x^{5} y^{5}}{y^{3} (3 x)}$

Step 5

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

Factor $3$ out of $6 x^{5} y^{5}$ .

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

Cancel the common factors.

Factor $3$ out of $y^{3} (3 x)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

Cancel the common factor of $x^{5}$ and $x$ .

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

$\frac{x (2 x^{4} y^{5})}{y^{3} (x)}$

Cancel the common factors.

Factor $x$ out of $y^{3} (x)$ .

$\frac{x (2 x^{4} y^{5})}{x y^{3}}$

Cancel the common factor.

$\frac{x (2 x^{4} y^{5})}{x y^{3}}$

Rewrite the expression.

$\frac{2 x^{4} y^{5}}{y^{3}}$

Step 7

Cancel the common factor of $y^{5}$ and $y^{3}$ .

Factor $y^{3}$ out of $2 x^{4} y^{5}$ .

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 x^{4} y^{2}$ by $1$ .

$2 x^{4} y^{2}$

Simplify (6x^3y)/(y^2)*(x^2y^4)/(3xy)

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