Simplify (3^(-2/3)*3^(1/3))^-1

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

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

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

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

Combine the numerators over the common denominator.

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

Add $- 2$ and $1$ .

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

Move the negative in front of the fraction.

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

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

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

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

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

Multiply $- 1$ by $- 1$ .

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

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.44224957 \dots$