Finite Math Examples

$\frac{1}{x \cdot x} = x^{9}$

Step 1

Subtract $x^{9}$ from both sides of the equation.

$\frac{1}{x \cdot x} - x^{9} = 0$

Step 2

Multiply $x$ by $x$ .

$\frac{1}{x^{2}} - x^{9} = 0$

Step 3

To write $- x^{9}$ as a fraction with a common denominator, multiply by $\frac{x^{2}}{x^{2}}$ .

$\frac{1}{x^{2}} - x^{9} \cdot \frac{x^{2}}{x^{2}} = 0$

Step 4

Combine $- x^{9}$ and $\frac{x^{2}}{x^{2}}$ .

$\frac{1}{x^{2}} + \frac{- x^{9} x^{2}}{x^{2}} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{1 - x^{9} x^{2}}{x^{2}} = 0$

Step 6

Multiply $x^{9}$ by $x^{2}$ by adding the exponents.

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Step 6.1

Move $x^{2}$ .

$\frac{1 - (x^{2} x^{9})}{x^{2}} = 0$

Step 6.2

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

$\frac{1 - x^{2 + 9}}{x^{2}} = 0$

Step 6.3

Add $2$ and $9$ .

$\frac{1 - x^{11}}{x^{2}} = 0$

Step 7

Set the numerator equal to zero.

$1 - x^{11} = 0$

Step 8

Solve the equation for $x$ .

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Step 8.1

Subtract $1$ from both sides of the equation.

$- x^{11} = - 1$

Step 8.2

Divide each term in $- x^{11} = - 1$ by $- 1$ and simplify.

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Step 8.2.1

Divide each term in $- x^{11} = - 1$ by $- 1$ .

$\frac{- x^{11}}{- 1} = \frac{- 1}{- 1}$

Step 8.2.2

Simplify the left side.

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Step 8.2.2.1

Dividing two negative values results in a positive value.

$\frac{x^{11}}{1} = \frac{- 1}{- 1}$

Step 8.2.2.2

Divide $x^{11}$ by $1$ .

$x^{11} = \frac{- 1}{- 1}$

Step 8.2.3

Simplify the right side.

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Step 8.2.3.1

Divide $- 1$ by $- 1$ .

$x^{11} = 1$

Step 8.3

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

$x = \sqrt[11]{1}$

Step 8.4

Any root of $1$ is $1$ .

$x = 1$