Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

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

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

Step 2

Cancel the common factor of $y$ and $y^{3}$ .

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Step 2.1

Factor $y$ out of $x y$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

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

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

Step 3

Apply basic rules of exponents.

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Step 3.1

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

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Multiply $2$ by $2$ .

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

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

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

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