The expression given in the image is $\left( \frac{2}{3} \right)^{-3}$.

Rewriting with a positive exponent:

To rewrite $\left( \frac{2}{3} \right)^{-3}$ using a positive exponent, apply the rule for negative exponents:

$a^{-n} = \frac{1}{a^n}$

So, $\left( \frac{2}{3} \right)^{-3} = \frac{1}{\left( \frac{2}{3} \right)^3}$.

Now, simplify $\left( \frac{2}{3} \right)^3$: $\left( \frac{2}{3} \right)^3 = \frac{2^3}{3^3} = \frac{8}{27}$

Thus, the expression becomes: $\frac{1}{\frac{8}{27}} = \frac{27}{8}$

Final Answer:

$\left( \frac{2}{3} \right)^{-3} = \frac{27}{8}$

Would you like further details or explanations on this?

Here are 5 related questions for further practice:

1. Rewrite $\left( \frac{4}{5} \right)^{-2}$ using positive exponents.
2. Simplify $\left( \frac{3}{7} \right)^{-4}$.
3. Rewrite $\left( \frac{5}{6} \right)^{-1}$ using positive exponents.
4. Evaluate $\left( \frac{7}{2} \right)^{-2}$ in its simplest form.
5. Simplify $\left( \frac{1}{4} \right)^{-3}$.

Tip: When dealing with negative exponents, remember that the base will be flipped and the exponent becomes positive.