Question

Simplify the expression (1/4ab)^-2. Assume a ≠ 0, b ≠ 0

Answer 1

Answer:

The expression $(\frac{1}{4ab})^{-2}$ is $16a^2b^2$

Step-by-step explanation:

Given :  the expression $(\frac{1}{4ab})^{-2}$

We have to simplify the given expression $(\frac{1}{4ab})^{-2}$

Consider the given expression $(\frac{1}{4ab})^{-2}$

Apply exponent rule $\left(\frac{a}{b}\right)^{-c}=\left(\left(\frac{a}{b}\right)^{-1}\right)^c=\left(\frac{b}{a}\right)^c$

We have,

$=\left(\frac{4ab}{1}\right)^2=\left(4ab\right)^2$

Apply exponent rule , $\left(a\cdot \:b\right)^n=a^nb^n$

$=4^2a^2b^2$

Simplify, we get,

$=16a^2b^2$

Thus, The expression $(\frac{1}{4ab})^{-2}$ is $16a^2b^2$

Answer 2

$( \dfrac{1}{4ab} )^{-2} = (4ab)^2 = 16a^2b^2$