The expression \((4x)^{-2}\) can be simplified by applying the property of exponents that states \(a^{-n} = \frac{1}{a^n}\).

Here's the step-by-step simplification:

\[
(4x)^{-2} = \frac{1}{(4x)^2}
\]

Next, we expand \((4x)^2\):

\[
(4x)^2 = 4^2 \times x^2 = 16x^2
\]

So, the expression simplifies to:

\[
\frac{1}{16x^2}
\]

Thus, \((4x)^{-2} = \frac{1}{16x^2}\).

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would you simplify \((2x^3)^{-1}\)?
2. What is the result of \((3y^{-2})^{-3}\)?
3. How does the expression \((2x)^{-2} \times (3y)^{-2}\) simplify?
4. Can you explain the difference between \((4x)^{-2}\) and \(4x^{-2}\)?
5. How do you simplify \(4x^{-2}\) and compare it to the initial problem?

**Tip:** When dealing with negative exponents, remember that they indicate the reciprocal of the base raised to the positive exponent.

Learn how to simplify the expression (4x)^-2 step-by-step with detailed explanations. This problem involves applying exponent rules, specifically the rule for negative exponents. Suitable for Grades 7-9 students seeking to understand exponent simplification.

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