Precalculus Examples

$\frac{6 a^{- 4} b^{- 3}}{9 a^{2} b^{- 2}}$

Step 1

Move $a^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{6 b^{- 3}}{9 a^{2} b^{- 2} a^{4}}$

Step 2

Move $b^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{6}{9 a^{2} b^{- 2} a^{4} b^{3}}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $a^{2}$ by $a^{4}$ by adding the exponents.

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Step 3.1.1

Move $a^{4}$ .

$\frac{6}{9 (a^{4} a^{2}) b^{- 2} b^{3}}$

Step 3.1.2

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

$\frac{6}{9 a^{4 + 2} b^{- 2} b^{3}}$

Step 3.1.3

Add $4$ and $2$ .

$\frac{6}{9 a^{6} b^{- 2} b^{3}}$

Step 3.2

Multiply $b^{- 2}$ by $b^{3}$ by adding the exponents.

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Step 3.2.1

Move $b^{3}$ .

$\frac{6}{9 a^{6} (b^{3} b^{- 2})}$

Step 3.2.2

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

$\frac{6}{9 a^{6} b^{3 - 2}}$

Step 3.2.3

Subtract $2$ from $3$ .

$\frac{6}{9 a^{6} b^{1}}$

Step 3.3

Simplify $9 a^{6} b^{1}$ .

$\frac{6}{9 a^{6} b}$

Step 4

Cancel the common factor of $6$ and $9$ .

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Step 4.1

Factor $3$ out of $6$ .

$\frac{3 (2)}{9 a^{6} b}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $9 a^{6} b$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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