Calculus Examples

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

Step 1

Multiply the exponents in ${(x^{- \frac{2}{3}})}^{2}$ .

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Step 1.1

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

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

Step 1.2

Multiply $- \frac{2}{3} \cdot 2$ .

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Step 1.2.1

Multiply $2$ by $- 1$ .

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

Step 1.2.2

Combine $- 2$ and $\frac{2}{3}$ .

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

Step 1.2.3

Multiply $- 2$ by $2$ .

$x^{\frac{- 4}{3}}$

Step 1.3

Move the negative in front of the fraction.

$x^{- \frac{4}{3}}$

Step 2

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

$\frac{1}{x^{\frac{4}{3}}}$