Evaluate (2y^3*3xy^3)/(3x^2y^4)

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

Step 1

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

Move $y^{3}$ .

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

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

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

Add $3$ and $3$ .

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

Step 2

Cancel the common factor of $y^{6}$ and $y^{4}$ .

Factor $y^{4}$ out of $2 y^{6} \cdot (3 x)$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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