To simplify the expression [tex]\(\left(\frac{1}{4ab}\right)^{-2}\)[/tex], we can follow the steps below:
1. Understand the given expression:
We start with the expression [tex]\(\left(\frac{1}{4ab}\right)^{-2}\)[/tex].
2. Use the properties of exponents:
When an expression in the form [tex]\(\left(\frac{1}{x}\right)^{-n}\)[/tex] is given, it can be rewritten as [tex]\(x^n\)[/tex]. So, [tex]\(\left(\frac{1}{4ab}\right)^{-2}\)[/tex] can be rewritten as:
[tex]\[
\left(4ab\right)^{2}
\][/tex]
3. Simplify the expression further:
Next, we need to expand [tex]\((4ab)^2\)[/tex] using the properties of exponents:
[tex]\[
(4ab)^2 = 4^2 \cdot a^2 \cdot b^2
\][/tex]
Evaluating [tex]\(4^2\)[/tex]:
[tex]\[
4^2 = 16
\][/tex]
4. Combine the terms:
Now we combine all the simplified terms:
[tex]\[
(4ab)^2 = 16a^2b^2
\][/tex]
Thus, the simplified form of the given expression [tex]\(\left(\frac{1}{4ab}\right)^{-2}\)[/tex] is [tex]\(16a^2b^2\)[/tex].
Therefore, the correct answer from the given choices is:
[tex]\[
\boxed{16a^2b^2}
\][/tex]
