If \({5}^{k^2}\times{25}^{2k}\times{625} = 25\times {\sqrt[4]{5}}\), which of the following is a possible value of \(k\)?

(A) \(-1\)

(B) \(-\Large\frac{1}{2}\)

(C) \(0\)

(D) \(\Large\frac{1}{2}\)

(E) \(1\)

If \({5}^{k^2}\times{25}^{2k}\times{625} = 25\times {\sqrt[4]{5}}\), which of the following is a possible value of \(k\)?

(A) \(-1\)

(B) \(-\Large\frac{1}{2}\)

(C) \(0\)

(D) \(\Large\frac{1}{2}\)

(E) \(1\)

I’m going to do a number of these posts. You can think of them as commentary on the 2016*Official Guide for GMAT Review.* I’m going to use the abbreviations OG, PS, DS, RC, CR, and SC for Official Guide, Problems Solving, Data Sufficiency, Reading Comprehension, Critical Reasoning, and Sentence Correction, respectively. Sometimes I’ll present alternative solutions, more detailed solutions, and, occasionally an example problem.

I can’t reproduce the problem here, so if you don’t have your official guide handy, now would be the time to break it out – page 175