Algebra Examples

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

Step 1

Multiply $3^{- \frac{2}{3}}$ by $3^{\frac{1}{3}}$ by adding the exponents.

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Step 1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 1.3

Add $- 2$ and $1$ .

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

Step 1.4

Move the negative in front of the fraction.

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

Step 2

Multiply the exponents in ${(3^{- \frac{1}{3}})}^{- 1}$ .

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

Multiply $- 1$ by $- 1$ .

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

Step 2.2.2

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

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