Question

Which of the following is not the reciprocal of ${\left(\frac{2}{3}\right)}^4$?

• A. ${\left(\frac{3}{2}\right)}^4$
• B. ${\left(\frac{2}{3}\right)}^{-4}$
• C. ${\left(\frac{3}{2}\right)}^{-4}$
• D. $\frac{3^4}{4^2}$

Answer 1

Answer: (C)

${\left(\frac{3}{2}\right)}^{-4}$

Reciprocal of $\frac{2}{3}=\frac{3}{2}$
we can write as
${\left(\frac{3}{2}\right)}^4={\left(\frac{3^2}{2^2}\right)}^2={\left(\frac{3}{2}\right)}^{-4}$
Hence, option $C$ is correct answer.