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Simplify: ( ( (1/x)^(-12))^(1/4))^(-2/3).

1. 1/x²
2. 1/x⁴
3. 1/x³
4. 1/x

Correct answer: 1/x²

Solution

Start inside: (1/x)^(-12) = x¹². Fourth root: (x¹²)^(1/4) = x³. Then raise to -2/3: (x³)^(-2/3) = x^(-2) = 1/x².

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