Pre-Algebra Examples

$\frac{6 a b}{a^{2} b^{2}} \cdot \frac{a^{2}}{b^{2}}$

Step 1

Combine.

$\frac{6 a b a^{2}}{a^{2} b^{2} b^{2}}$

Step 2

Multiply $a$ by $a^{2}$ by adding the exponents.

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Step 2.1

Move $a^{2}$ .

$\frac{6 (a^{2} a) b}{a^{2} b^{2} b^{2}}$

Step 2.2

Multiply $a^{2}$ by $a$ .

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Step 2.2.1

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

$\frac{6 (a^{2} a^{1}) b}{a^{2} b^{2} b^{2}}$

Step 2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{6 a^{2 + 1} b}{a^{2} b^{2} b^{2}}$

Step 2.3

Add $2$ and $1$ .

$\frac{6 a^{3} b}{a^{2} b^{2} b^{2}}$

Step 3

Multiply $b^{2}$ by $b^{2}$ by adding the exponents.

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Step 3.1

Move $b^{2}$ .

$\frac{6 a^{3} b}{a^{2} (b^{2} b^{2})}$

Step 3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{6 a^{3} b}{a^{2} b^{2 + 2}}$

Step 3.3

Add $2$ and $2$ .

$\frac{6 a^{3} b}{a^{2} b^{4}}$

Step 4

Cancel the common factor of $a^{3}$ and $a^{2}$ .

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Step 4.1

Factor $a^{2}$ out of $6 a^{3} b$ .

$\frac{a^{2} (6 a b)}{a^{2} b^{4}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a^{2}$ out of $a^{2} b^{4}$ .

$\frac{a^{2} (6 a b)}{a^{2} (b^{4})}$

Step 4.2.2

Cancel the common factor.

$\frac{a^{2} (6 a b)}{a^{2} b^{4}}$

Step 4.2.3

Rewrite the expression.

$\frac{6 a b}{b^{4}}$

Step 5

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

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Step 5.1

Factor $b$ out of $6 a b$ .

$\frac{b (6 a)}{b^{4}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $b$ out of $b^{4}$ .

$\frac{b (6 a)}{b \cdot b^{3}}$

Step 5.2.2

Cancel the common factor.

$\frac{b (6 a)}{b \cdot b^{3}}$

Step 5.2.3

Rewrite the expression.

$\frac{6 a}{b^{3}}$