Respuesta :
Answer:
The expression [tex](\frac{1}{4ab})^{-2}[/tex] is [tex]16a^2b^2[/tex]
Step-by-step explanation:
Given : the expression [tex](\frac{1}{4ab})^{-2}[/tex]
We have to simplify the given expression [tex](\frac{1}{4ab})^{-2}[/tex]
Consider the given expression [tex](\frac{1}{4ab})^{-2}[/tex]
Apply exponent rule [tex]\left(\frac{a}{b}\right)^{-c}=\left(\left(\frac{a}{b}\right)^{-1}\right)^c=\left(\frac{b}{a}\right)^c[/tex]
We have,
[tex]=\left(\frac{4ab}{1}\right)^2=\left(4ab\right)^2[/tex]
Apply exponent rule , [tex]\left(a\cdot \:b\right)^n=a^nb^n[/tex]
[tex]=4^2a^2b^2[/tex]
Simplify, we get,
[tex]=16a^2b^2[/tex]
Thus, The expression [tex](\frac{1}{4ab})^{-2}[/tex] is [tex]16a^2b^2[/tex]
