If m is an integer and x^m = 1/x^m, what is the value of x?

Target question: What is the value of x?

Given: m is an integer and \(x^m = \frac{1}{x^m}\)
When we see the equation \(x^m = \frac{1}{x^m}\), we should ask ourselves "Under what circumstances can \(x^m\) equal \(\frac{1}{x^m}\)?"
A few of circumstances include:
I. \(x =\) any non-zero integer, and \(m = 0\), in which case the given equation of satisfied.
II. \(x = 1\), and \(m =\) any integer, in which case the given equation of satisfied.
III. \(x = -1\), and \(m =\) any even integer, in which case the given equation of satisfied.

Once we see the two statements, we can eliminate case I, but cases II and III remain, which means we can jump straight to . . .

Statements 1 and 2 combined
There are several values of m and x that satisfy BOTH statements. Here are two:
Case a: \(x = 1\) and \(m = 1\). In this case, the answer to the target question is \(x = 1\)
Case b: \(x = -1\) and \(m = 2\). In this case, the answer to the target question is \(x = -1\)
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E