Calculus Examples

$\frac{1}{5 x^{- 6}} \cdot x^{- 2} - 1^{- 2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{5 \frac{1}{x^{6}}} \cdot x^{- 2} - 1^{- 2}$

Step 1.2

Combine $5$ and $\frac{1}{x^{6}}$ .

$\frac{1}{\frac{5}{x^{6}}} \cdot x^{- 2} - 1^{- 2}$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{x^{6}}{5} \cdot x^{- 2} - 1^{- 2}$

Step 1.4

Multiply $\frac{x^{6}}{5}$ by $1$ .

$\frac{x^{6}}{5} \cdot x^{- 2} - 1^{- 2}$

Step 1.5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{6}}{5} \cdot \frac{1}{x^{2}} - 1^{- 2}$

Step 1.6

Combine.

$\frac{x^{6} \cdot 1}{5 x^{2}} - 1^{- 2}$

Step 1.7

Cancel the common factor of $x^{6}$ and $x^{2}$ .

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Step 1.7.1

Factor $x^{2}$ out of $x^{6} \cdot 1$ .

$\frac{x^{2} (x^{4} \cdot 1)}{5 x^{2}} - 1^{- 2}$

Step 1.7.2

Cancel the common factors.

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Step 1.7.2.1

Factor $x^{2}$ out of $5 x^{2}$ .

$\frac{x^{2} (x^{4} \cdot 1)}{x^{2} \cdot 5} - 1^{- 2}$

Step 1.7.2.2

Cancel the common factor.

$\frac{x^{2} (x^{4} \cdot 1)}{x^{2} \cdot 5} - 1^{- 2}$

Step 1.7.2.3

Rewrite the expression.

$\frac{x^{4} \cdot 1}{5} - 1^{- 2}$

Step 1.8

Multiply $x^{4}$ by $1$ .

$\frac{x^{4}}{5} - 1^{- 2}$

Step 1.9

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{4}}{5} - \frac{1}{1^{2}}$

Step 1.10

One to any power is one.

$\frac{x^{4}}{5} - \frac{1}{1}$

Step 1.11

Cancel the common factor of $1$ .

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Step 1.11.1

Cancel the common factor.

$\frac{x^{4}}{5} - \frac{1}{1}$

Step 1.11.2

Rewrite the expression.

$\frac{x^{4}}{5} - 1 \cdot 1$

Step 1.12

Multiply $- 1$ by $1$ .

$\frac{x^{4}}{5} - 1$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x^{4}}{5} - 1 \cdot \frac{5}{5}$

Step 3

Combine $- 1$ and $\frac{5}{5}$ .

$\frac{x^{4}}{5} + \frac{- 1 \cdot 5}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{x^{4} - 1 \cdot 5}{5}$

Step 5

Multiply $- 1$ by $5$ .

$\frac{x^{4} - 5}{5}$