Precalculus Examples

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

Step 1

Move $a^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Simplify the numerator.

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Step 2.1

Factor $3 a^{- 2}$ out of $6 a^{- 2} + 9 a^{2}$ .

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Step 2.1.1

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

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

Step 2.1.2

Factor $3 a^{- 2}$ out of $9 a^{2}$ .

$\frac{(3 a^{- 2} (2) + 3 a^{- 2} (3 a^{4})) a^{2}}{3}$

Step 2.1.3

Factor $3 a^{- 2}$ out of $3 a^{- 2} (2) + 3 a^{- 2} (3 a^{4})$ .

$\frac{3 a^{- 2} (2 + 3 a^{4}) a^{2}}{3}$

Step 2.2

Combine exponents.

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Step 2.2.1

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

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Step 2.2.1.1

Move $a^{2}$ .

$\frac{3 (a^{2} a^{- 2}) (2 + 3 a^{4})}{3}$

Step 2.2.1.2

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

$\frac{3 a^{2 - 2} (2 + 3 a^{4})}{3}$

Step 2.2.1.3

Subtract $2$ from $2$ .

$\frac{3 a^{0} (2 + 3 a^{4})}{3}$

Step 2.2.2

Simplify $3 a^{0} (2 + 3 a^{4})$ .

$\frac{3 (2 + 3 a^{4})}{3}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$\frac{3 (2 + 3 a^{4})}{3}$

Step 3.2

Divide $2 + 3 a^{4}$ by $1$ .

$2 + 3 a^{4}$