Calculus Examples

${(- \frac{1}{8})}^{- \frac{5}{3}}$

Step 1

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

${(- 8)}^{\frac{5}{3}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $- 8$ as ${(- 2)}^{3}$ .

${({(- 2)}^{3})}^{\frac{5}{3}}$

Step 2.2

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

${(- 2)}^{3 (\frac{5}{3})}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

${(- 2)}^{3 (\frac{5}{3})}$

Step 3.2

Rewrite the expression.

${(- 2)}^{5}$

Step 4

Raise $- 2$ to the power of $5$ .

$- 32$