Calculus Examples

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

Step 1

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

$x^{\frac{1}{3} - 1 \cdot \frac{3}{3}}$

Step 2

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

$x^{\frac{1}{3} + \frac{- 1 \cdot 3}{3}}$

Step 3

Combine the numerators over the common denominator.

$x^{\frac{1 - 1 \cdot 3}{3}}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $- 1$ by $3$ .

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

Step 4.2

Subtract $3$ from $1$ .

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

Step 5

Move the negative in front of the fraction.

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

Step 6

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

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