Question:
Which of the following is not 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) $\frac{3^{4}}{2^{4}}$
Solution:
(c) $\left(\frac{3}{2}\right)^{-4}$
The reciprocal of $\left(\frac{2}{3}\right)^{4}$ is $\left(\frac{3}{2}\right)^{4}$.
Therefore, option (a) is the correct answer.
Option (b) is just re-expressing the number with a negative exponent.
Option (d) is obtained by working out the exponent.
Hence, option (c) is not the reciprocal of $\left(\frac{2}{3}\right)^{4}$.
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