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The expression you provided is:

\[
\left( \frac{2}{3} \right)^{-4}
\]

To simplify this, we apply the property of exponents that states:

\[
\left( \frac{a}{b} \right)^{-n} = \left( \frac{b}{a} \right)^{n}
\]

Using this property:

\[
\left( \frac{2}{3} \right)^{-4} = \left( \frac{3}{2} \right)^4
\]

Now, raising \(\frac{3}{2}\) to the power of 4:

\[
\left( \frac{3}{2} \right)^4 = \frac{3^4}{2^4} = \frac{81}{16}
\]

Thus, the simplified result is:

\[
\left( \frac{2}{3} \right)^{-4} = \frac{81}{16}
\]

Would you like further details or have any questions? Here are five related questions to explore:

1. How do negative exponents work for other fractions?
2. What is the general rule for exponents of negative numbers?
3. How can you simplify expressions like \(\left( \frac{5}{7} \right)^{-2}\)?
4. What is the difference between raising a fraction to a negative exponent versus a positive exponent?
5. How do these exponent rules apply when dealing with variables instead of constants?

**Tip:** Always remember, raising a fraction to a negative exponent inverts the fraction before applying the power!

Learn how to simplify the expression (2/3)^-4 by applying the exponent rules. This example involves inverting the fraction and raising it to the power of 4, yielding 81/16. Suitable for students in Grades 8-10.

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