Simplify ((-3xy^3)^2)/((2xy)*(6y^3))

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

Step 1

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

Move $y^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

Step 2

Simplify the numerator.

Apply the product rule to $- 3 x y^{3}$ .

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

Apply the product rule to $- 3 x$ .

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

Raise $- 3$ to the power of $2$ .

$\frac{9 x^{2} {(y^{3})}^{2}}{2 x y^{4} \cdot 6}$

Multiply the exponents in ${(y^{3})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{9 x^{2} y^{3 \cdot 2}}{2 x y^{4} \cdot 6}$

Multiply $3$ by $2$ .

$\frac{9 x^{2} y^{6}}{2 x y^{4} \cdot 6}$

Step 3

Reduce the expression by cancelling the common factors.

Multiply $6$ by $2$ .

$\frac{9 x^{2} y^{6}}{12 x y^{4}}$

Cancel the common factor of $9$ and $12$ .

Factor $3$ out of $9 x^{2} y^{6}$ .

$\frac{3 (3 x^{2} y^{6})}{12 x y^{4}}$

Cancel the common factors.

Factor $3$ out of $12 x y^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Factor $x$ out of $3 x^{2} y^{6}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify ((-3xy^3)^2)/((2xy)*(6y^3))

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