Simplify (12(xy^2)^2)/(4xy^2)

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

Step 1

Cancel the common factor of $12$ and $4$ .

Factor $4$ out of $12 {(x y^{2})}^{2}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Simplify the numerator.

Apply the product rule to $x y^{2}$ .

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

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

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

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

Multiply $2$ by $2$ .

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

Step 3

Reduce the expression by cancelling the common factors.

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y^{4}$ and $y^{2}$ .

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

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 x y^{2}}{1}$

Divide $3 x y^{2}$ by $1$ .

$3 x y^{2}$