Question

Which of the following is equal to ${(-\frac{3}{4})}^{-3}$?

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

Answer 1

The correct option is D

${(-\frac{4}{3})}^3$

Step 1. Explanation for the correct option:

Option (D): ${(-\frac{4}{3})}^3$

$$\begin{gathered} {\left(-\frac{3}{4}\right)}^{-3}=\frac{1}{{\left(-\frac{3}{4}\right)}^3}\left[\because a^{-1}=\frac{1}{a}\right] \\ ={\left(-\frac{4}{3}\right)}^3 \end{gathered}$$

Hence, “Option D” is the correct option.

Step 2. Explanation for the incorrect options.

Option (A): ${\left(\frac{3}{4}\right)}^{-3}$

$$\begin{gathered} {\left(\frac{3}{4}\right)}^{-3}=\frac{1}{{\left({\displaystyle \frac{3}{4}}\right)}^3}\left[\because a^{-1}=\frac{1}{a}\right] \\ ={\left(\frac{4}{3}\right)}^3 \end{gathered}$$

The value mentioned in Option A is not equal to the value determined above

Hence, “Option A” is the incorrect option.

Option (B): $-{\left(\frac{3}{4}\right)}^{-3}$

$$\begin{gathered} -{\left(\frac{3}{4}\right)}^{-3}=-\frac{1}{{\left(\frac{3}{4}\right)}^3}\left[\because a^{-1}=\frac{1}{a}\right] \\ ={-\left(\frac{4}{3}\right)}^3 \end{gathered}$$

Thus the value mentioned in Option B is not equal to the value determined above

Hence, “Option B” is the incorrect option.

Option (C): ${\left(\frac{4}{3}\right)}^3$

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

Hence, the value mentioned in Option C is not equal to the value determined above

Hence, “Option D” is the correct option.