Variable w/ exponents DS theory question

[JeffreyB581]

Started thinking about this question and wanted to double check my thought process.

x^-2 = ?

Restated: (1/x)^2=?

Statement 1: x^-1 = 1/2
Sufficient: x^1=2, therefore x^2=4, therefore x^-2=1/4

Statement 2: x^2=4?
Sufficient: x can be both +/- 2, but this does not change the fact that x^-2=1/4

My question is this: If the original statement was x^-3=?
Statement 1 would still be valid but statement 2 would not because the odd exponent requires that you know the sign. The answer could be 1/8 or -1/8. Is my thinking correct here?

[RonPurewal]

hi,
per the forum rules, please cite the original source of this problem. thank you.