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

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

Step 1

Simplify the numerator.

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

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

Apply the product rule to $2 x$ .

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

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

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

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

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

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

Multiply $2$ by $2$ .

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

Step 2

Simplify the denominator.

Apply the product rule to $x^{2} y^{3}$ .

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

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

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

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

Multiply $2$ by $2$ .

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

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

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

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

Multiply $3$ by $2$ .

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

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factors.

Factor $x^{2}$ out of $x^{4} y^{6}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Multiply by $1$ .

$\frac{y^{4} \cdot 1}{x^{2} y^{6}}$

Cancel the common factors.

Factor $y^{4}$ out of $x^{2} y^{6}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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