Finite Math Examples

$20 x^{- 2} x^{- 1} - 1 = 0$

Step 1

Multiply $x^{- 2}$ by $x^{- 1}$ by adding the exponents.

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Step 1.1

Move $x^{- 1}$ .

$20 (x^{- 1} x^{- 2}) - 1 = 0$

Step 1.2

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

$20 x^{- 1 - 2} - 1 = 0$

Step 1.3

Subtract $2$ from $- 1$ .

$20 x^{- 3} - 1 = 0$

Step 2

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

$20 (\frac{1}{x^{3}}) - 1 = 0$

Step 3

Combine $20$ and $\frac{1}{x^{3}}$ .

$\frac{20}{x^{3}} - 1 = 0$

Step 4

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{x^{3}}{x^{3}}$ .

$\frac{20}{x^{3}} - 1 \cdot \frac{x^{3}}{x^{3}} = 0$

Step 5

Combine $- 1$ and $\frac{x^{3}}{x^{3}}$ .

$\frac{20}{x^{3}} + \frac{- x^{3}}{x^{3}} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{20 - x^{3}}{x^{3}} = 0$

Step 7

Set the numerator equal to zero.

$20 - x^{3} = 0$

Step 8

Solve the equation for $x$ .

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Step 8.1

Subtract $20$ from both sides of the equation.

$- x^{3} = - 20$

Step 8.2

Divide each term in $- x^{3} = - 20$ by $- 1$ and simplify.

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Step 8.2.1

Divide each term in $- x^{3} = - 20$ by $- 1$ .

$\frac{- x^{3}}{- 1} = \frac{- 20}{- 1}$

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.

$\frac{x^{3}}{1} = \frac{- 20}{- 1}$

Step 8.2.2.2

Divide $x^{3}$ by $1$ .

$x^{3} = \frac{- 20}{- 1}$

Step 8.2.3

Simplify the right side.

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Step 8.2.3.1

Divide $- 20$ by $- 1$ .

$x^{3} = 20$

Step 8.3

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

$x = \sqrt[3]{20}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt[3]{20}$

Decimal Form:

$x = 2.71441761 \dots$