Precalculus Examples

$\frac{8 n^{4} - 4 n^{- 2}}{2 n^{- 2}}$

Step 1

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

$\frac{(8 n^{4} - 4 n^{- 2}) n^{2}}{2}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $4 n^{- 2}$ out of $8 n^{4} - 4 n^{- 2}$ .

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Step 2.1.1

Factor $4 n^{- 2}$ out of $8 n^{4}$ .

$\frac{(4 n^{- 2} (2 n^{6}) - 4 n^{- 2}) n^{2}}{2}$

Step 2.1.2

Factor $4 n^{- 2}$ out of $- 4 n^{- 2}$ .

$\frac{(4 n^{- 2} (2 n^{6}) + 4 n^{- 2} (- 1)) n^{2}}{2}$

Step 2.1.3

Factor $4 n^{- 2}$ out of $4 n^{- 2} (2 n^{6}) + 4 n^{- 2} (- 1)$ .

$\frac{4 n^{- 2} (2 n^{6} - 1) n^{2}}{2}$

Step 2.2

Combine exponents.

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Step 2.2.1

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

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Step 2.2.1.1

Move $n^{2}$ .

$\frac{4 (n^{2} n^{- 2}) (2 n^{6} - 1)}{2}$

Step 2.2.1.2

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

$\frac{4 n^{2 - 2} (2 n^{6} - 1)}{2}$

Step 2.2.1.3

Subtract $2$ from $2$ .

$\frac{4 n^{0} (2 n^{6} - 1)}{2}$

Step 2.2.2

Simplify $4 n^{0} (2 n^{6} - 1)$ .

$\frac{4 (2 n^{6} - 1)}{2}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $4$ and $2$ .

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Step 3.1.1

Factor $2$ out of $4 (2 n^{6} - 1)$ .

$\frac{2 (2 (2 n^{6} - 1))}{2}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $2$ out of $2$ .

$\frac{2 (2 (2 n^{6} - 1))}{2 (1)}$

Step 3.1.2.2

Cancel the common factor.

$\frac{2 (2 (2 n^{6} - 1))}{2 \cdot 1}$

Step 3.1.2.3

Rewrite the expression.

$\frac{2 (2 n^{6} - 1)}{1}$

Step 3.1.2.4

Divide $2 (2 n^{6} - 1)$ by $1$ .

$2 (2 n^{6} - 1)$

Step 3.2

Apply the distributive property.

$2 (2 n^{6}) + 2 \cdot - 1$

Step 3.3

Multiply.

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Step 3.3.1

Multiply $2$ by $2$ .

$4 n^{6} + 2 \cdot - 1$

Step 3.3.2

Multiply $2$ by $- 1$ .

$4 n^{6} - 2$