Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

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 $x$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

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 $y$ .

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $y$ out of $3 y$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

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.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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.

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Step 5.1

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

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

Step 5.2

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

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Step 5.2.1

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

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

Step 5.2.2

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 $2$ .

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$