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

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

Step 1

Cancel the common factor of $4$ and $6$ .

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

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

Cancel the common factors.

Factor $2$ out of $6 x y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 2

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

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

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

Cancel the common factors.

Factor $x$ out of $3 x y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 3

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

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

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

Cancel the common factors.

Factor $y$ out of $3 y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

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

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

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

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

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

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

Step 5

Simplify the numerator.

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

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

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

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

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

Multiply $3$ by $2$ .

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

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

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

Step 6

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

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

Related Questions