Calculus Examples

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

Step 1

Move $27^{\frac{- 1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Move the negative in front of the fraction.

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

Step 3

Multiply $- - \frac{1}{3}$ .

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Step 3.1

Multiply $- 1$ by $- 1$ .

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

Step 3.2

Multiply $\frac{1}{3}$ by $1$ .

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

Step 4

Simplify the expression.

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Step 4.1

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

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

Step 4.2

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

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

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$3^{1}$

Step 6

Evaluate the exponent.

$3$