Question

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

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

Answer 1

The correct option is A

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

Explanation.

The reciprocal of a number $a$ is $\frac{1}{a}$.

The reciprocal of ${\left(\frac{2}{3}\right)}^4$ is

$$\begin{gathered} \frac{1}{{\left(\frac{2}{3}\right)}^4}=\frac{1}{\frac{2^4}{3^4}} \\ =\frac{3^4}{2^4} \\ ={\left(\frac{3}{2}\right)}^4 \end{gathered}$$

Hence, the correct option is $\mathrm{A}$.