Pre-Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $x$ out of $x y$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Raise $y$ to the power of $1$ .

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

Step 2.2.2

Factor $y$ out of $y^{1}$ .

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

Step 2.2.3

Cancel the common factor.

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

Step 2.2.4

Rewrite the expression.

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

Step 2.2.5

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

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

Step 3

Apply basic rules of exponents.

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Step 3.1

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

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Multiply $2$ by $2$ .

$x^{4} {(y^{2})}^{2}$

Step 3.3

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

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Step 3.3.1

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

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

Step 3.3.2

Multiply $2$ by $2$ .

$x^{4} y^{4}$