Calculus Examples

$x^{- 2} = 1$

Step 1

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

$\frac{1}{x^{2}} = 1$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x^{2}, 1$

Step 2.2

The LCM of one and any expression is the expression.

$x^{2}$

Step 3

Multiply each term in $\frac{1}{x^{2}} = 1$ by $x^{2}$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{1}{x^{2}} = 1$ by $x^{2}$ .

$\frac{1}{x^{2}} x^{2} = 1 x^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

Cancel the common factor.

$\frac{1}{x^{2}} x^{2} = 1 x^{2}$

Step 3.2.1.2

Rewrite the expression.

$1 = 1 x^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $x^{2}$ by $1$ .

$1 = x^{2}$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $x^{2} = 1$ .

$x^{2} = 1$

Step 4.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{1}$

Step 4.3

Any root of $1$ is $1$ .

$x = \pm 1$

Step 4.4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.4.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 1$

Step 4.4.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 1$

Step 4.4.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 1, - 1$