Finite Math Examples

$6 u^{- \frac{1}{3}} = - 9$

Step 1

Divide each term in $6 u^{- \frac{1}{3}} = - 9$ by $6$ and simplify.

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Step 1.1

Divide each term in $6 u^{- \frac{1}{3}} = - 9$ by $6$ .

$\frac{6 u^{- \frac{1}{3}}}{6} = \frac{- 9}{6}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Move $u^{- \frac{1}{3}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{6}{6 u^{\frac{1}{3}}} = \frac{- 9}{6}$

Step 1.2.2

Cancel the common factor.

$\frac{6}{6 u^{\frac{1}{3}}} = \frac{- 9}{6}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{u^{\frac{1}{3}}} = \frac{- 9}{6}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $- 9$ and $6$ .

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Step 1.3.1.1

Factor $3$ out of $- 9$ .

$\frac{1}{u^{\frac{1}{3}}} = \frac{3 (- 3)}{6}$

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $3$ out of $6$ .

$\frac{1}{u^{\frac{1}{3}}} = \frac{3 \cdot - 3}{3 \cdot 2}$

Step 1.3.1.2.2

Cancel the common factor.

$\frac{1}{u^{\frac{1}{3}}} = \frac{3 \cdot - 3}{3 \cdot 2}$

Step 1.3.1.2.3

Rewrite the expression.

$\frac{1}{u^{\frac{1}{3}}} = \frac{- 3}{2}$

Step 1.3.2

Move the negative in front of the fraction.

$\frac{1}{u^{\frac{1}{3}}} = - \frac{3}{2}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$1 \cdot 2 = u^{\frac{1}{3}} \cdot - 3$

Step 3

Solve the equation for $u$ .

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Step 3.1

Rewrite the equation as $u^{\frac{1}{3}} \cdot - 3 = 1 \cdot 2$ .

$u^{\frac{1}{3}} \cdot - 3 = 1 \cdot 2$

Step 3.2

Multiply $2$ by $1$ .

$u^{\frac{1}{3}} \cdot - 3 = 2$

Step 3.3

Divide each term in $u^{\frac{1}{3}} \cdot - 3 = 2$ by $- 3$ and simplify.

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Step 3.3.1

Divide each term in $u^{\frac{1}{3}} \cdot - 3 = 2$ by $- 3$ .

$\frac{u^{\frac{1}{3}} \cdot - 3}{- 3} = \frac{2}{- 3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor.

$\frac{u^{\frac{1}{3}} \cdot - 3}{- 3} = \frac{2}{- 3}$

Step 3.3.2.2

Divide $u^{\frac{1}{3}}$ by $1$ .

$u^{\frac{1}{3}} = \frac{2}{- 3}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Move the negative in front of the fraction.

$u^{\frac{1}{3}} = - \frac{2}{3}$

Step 3.4

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${(u^{\frac{1}{3}})}^{3} = {(- \frac{2}{3})}^{3}$

Step 3.5

Simplify the exponent.

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Step 3.5.1

Simplify the left side.

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Step 3.5.1.1

Simplify ${(u^{\frac{1}{3}})}^{3}$ .

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Step 3.5.1.1.1

Multiply the exponents in ${(u^{\frac{1}{3}})}^{3}$ .

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Step 3.5.1.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$u^{\frac{1}{3} \cdot 3} = {(- \frac{2}{3})}^{3}$

Step 3.5.1.1.1.2

Cancel the common factor of $3$ .

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Step 3.5.1.1.1.2.1

Cancel the common factor.

$u^{\frac{1}{3} \cdot 3} = {(- \frac{2}{3})}^{3}$

Step 3.5.1.1.1.2.2

Rewrite the expression.

$u^{1} = {(- \frac{2}{3})}^{3}$

Step 3.5.1.1.2

Simplify.

$u = {(- \frac{2}{3})}^{3}$

Step 3.5.2

Simplify the right side.

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Step 3.5.2.1

Simplify ${(- \frac{2}{3})}^{3}$ .

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Step 3.5.2.1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.5.2.1.1.1

Apply the product rule to $- \frac{2}{3}$ .

$u = {(- 1)}^{3} {(\frac{2}{3})}^{3}$

Step 3.5.2.1.1.2

Apply the product rule to $\frac{2}{3}$ .

$u = {(- 1)}^{3} \frac{2^{3}}{3^{3}}$

Step 3.5.2.1.2

Raise $- 1$ to the power of $3$ .

$u = - \frac{2^{3}}{3^{3}}$

Step 3.5.2.1.3

Raise $2$ to the power of $3$ .

$u = - \frac{8}{3^{3}}$

Step 3.5.2.1.4

Raise $3$ to the power of $3$ .

$u = - \frac{8}{27}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$u = - \frac{8}{27}$

Decimal Form:

$u = - 0.\overline{296}$