Finite Math Examples

${(\frac{- 8}{27})}^{- \frac{1}{3}}$

Step 1

Move the negative in front of the fraction.

${(- \frac{8}{27})}^{- \frac{1}{3}}$

Step 2

Change the sign of the exponent by rewriting the base as its reciprocal.

${(- \frac{27}{8})}^{\frac{1}{3}}$

Step 3

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

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Step 3.1

Apply the product rule to $- \frac{27}{8}$ .

${(- 1)}^{\frac{1}{3}} {(\frac{27}{8})}^{\frac{1}{3}}$

Step 3.2

Apply the product rule to $\frac{27}{8}$ .

${(- 1)}^{\frac{1}{3}} \frac{27^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 4

Simplify the expression.

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Step 4.1

Rewrite $- 1$ as ${(- 1)}^{3}$ .

${({(- 1)}^{3})}^{\frac{1}{3}} \frac{27^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 4.2

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

${(- 1)}^{3 (\frac{1}{3})} \frac{27^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Cancel the common factor.

${(- 1)}^{3 (\frac{1}{3})} \frac{27^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 5.2

Rewrite the expression.

${(- 1)}^{1} \frac{27^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 6

Evaluate the exponent.

$- \frac{27^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 7

Simplify the numerator.

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Step 7.1

Rewrite $27$ as $3^{3}$ .

$- \frac{{(3^{3})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Step 7.2

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

$- \frac{3^{3 (\frac{1}{3})}}{8^{\frac{1}{3}}}$

Step 7.3

Cancel the common factor of $3$ .

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Step 7.3.1

Cancel the common factor.

$- \frac{3^{3 (\frac{1}{3})}}{8^{\frac{1}{3}}}$

Step 7.3.2

Rewrite the expression.

$- \frac{3^{1}}{8^{\frac{1}{3}}}$

Step 7.4

Evaluate the exponent.

$- \frac{3}{8^{\frac{1}{3}}}$

Step 8

Simplify the denominator.

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Step 8.1

Rewrite $8$ as $2^{3}$ .

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

Step 8.2

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

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

Step 8.3

Cancel the common factor of $3$ .

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Step 8.3.1

Cancel the common factor.

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

Step 8.3.2

Rewrite the expression.

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

Step 8.4

Evaluate the exponent.

$- \frac{3}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{2}$

Decimal Form:

$- 1.5$

Mixed Number Form:

$- 1 \frac{1}{2}$