What is (x^2) times blank exponent that equal x?

Answer 1

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[ x² ] ^(1/2) = x IF x ≥ 0

Answer 2

The answer is 1/2 because (x^2)^(1/2) = x^(2/2) = x

Another approach:

(x^2)^n = x

x^(2n) = x

Since the bases are the same, we can set the exponents equal to each other:

2n = 1

n = 1/2, where x ≥ 0