To simplify the expression [tex]\(\left(\frac{1}{4ab}\right)^{-2}\)[/tex], let's go through it step by step.
1. Understanding Negative Exponents: The expression [tex]\(\left(\frac{1}{4ab}\right)^{-2}\)[/tex] involves a negative exponent. Recall that: [tex]\[
(x^{-n}) = \frac{1}{x^n}
\][/tex] and [tex]\[
\left(\frac{1}{x}\right)^{-n} = x^n
\][/tex] Therefore, [tex]\[
\left(\frac{1}{4ab}\right)^{-2} = (4ab)^2
\][/tex]
2. Applying the Exponent: Now, we need to square the term inside the parentheses: [tex]\[
(4ab)^2
\][/tex]
3. Exponent Distributes Over Multiplication: When raising a product to an exponent, apply the exponent to each factor inside: [tex]\[
(4ab)^2 = 4^2 \cdot (a)^2 \cdot (b)^2
\][/tex]
