Question

Which of the following is not equal to ${\left(\frac{-5}{4}\right)}^4$?

• A. $\frac{{\left(-5\right)}^4}{4^4}$
• B. $\frac{5^4}{{\left(-4\right)}^4}$
• C. $-\left(\frac{5^4}{4^4}\right)$
• D. $\left(-\frac{5}{4}\right)\times \left(-\frac{5}{4}\right)\times \left(-\frac{5}{4}\right)\times \left(-\frac{5}{4}\right)$

Answer 1

The correct option is C

$-\left(\frac{5^4}{4^4}\right)$

Step 1. Explanation for the correct option.

Simplify:

$$\begin{gathered} {\left(\frac{-5}{4}\right)}^4=\left(-1^4\right)\times {\left(\frac{5}{4}\right)}^4 \\ ={\left(\frac{5}{4}\right)}^4 \end{gathered}$$

Now,

${\left(\frac{-5}{4}\right)}^4\ne -{\left(\frac{5}{4}\right)}^4$

Step 2. Explanation for the incorrect options.

$$\begin{gathered} \frac{{\left(-5\right)}^4}{4^4}={\left(\frac{-5}{4}\right)}^4 \\ \frac{5^4}{{\left(-4\right)}^4}={\left(\frac{-5}{4}\right)}^4 \end{gathered}$$

And

$\left(-\frac{5}{4}\right)\times \left(-\frac{5}{4}\right)\times \left(-\frac{5}{4}\right)\times \left(-\frac{5}{4}\right)={\left(-\frac{5}{4}\right)}^4$

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