Bunuel wrote:

Official Solution:

If \(@x= \frac{x^x}{2x^2}-2\), what is the units digit of \(@(@4)\)?

A. 1

B. 3

C. 4

D. 6

E. 8

First of all \(\frac{x^x}{2x^2}-2 = \frac{x^{x-2}}{2}-2\), so \(@4=\frac{4^{4-2}}{2}-2=6\);

Next, \(@6=\frac{6^{6-2}}{2}-2=\frac{6^{4}}{2}-2=\frac{6*6^{3}}{2}-2=3*6^3-2\). Now, the units digit of \(6^3\) is 6, thus the units digit of \(3*6^3\) is 8 (\(3*6=18\)), so the units digit of \(3*6^3-2\) is \(8-2=6\).

Answer: D

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how u got this:

\(\frac{x^x}{2x^2}-2 = \frac{x^{x-2}}{2}-2\)