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

User Loomer
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2 Answers

1 vote

( (1)/(4ab) )^(-2) = (4ab)^2 = 16a^2b^2
User Wymli
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2 votes

Answer:

The expression
((1)/(4ab))^(-2) is
16a^2b^2

Explanation:

Given : the expression
((1)/(4ab))^(-2)

We have to simplify the given expression
((1)/(4ab))^(-2)

Consider the given expression
((1)/(4ab))^(-2)

Apply exponent rule
\left((a)/(b)\right)^(-c)=\left(\left((a)/(b)\right)^(-1)\right)^c=\left((b)/(a)\right)^c

We have,


=\left((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
((1)/(4ab))^(-2) is
16a^2b^2

User Yulric Sequeira
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6.0k points