1. The problem is to find the value of $(\frac{2}{3})^{-1}$. 2. Recall the rule for negative exponents: For any nonzero number $a$ and integer $n$, $a^{-n} = \frac{1}{a^n}$. 3. Applying this rule, we have: $$\left(\frac{2}{3}\right)^{-1} = \frac{1}{\frac{2}{3}}$$ 4. Dividing by a fraction is the same as multiplying by its reciprocal: $$\frac{1}{\frac{2}{3}} = 1 \times \frac{3}{2} = \frac{3}{2}$$ 5. Therefore, the value of $(\frac{2}{3})^{-1}$ is $\frac{3}{2}$. This means that raising a fraction to the power of $-1$ flips the numerator and denominator.