Problems when multiplying powers

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 In the past I used to confuse students by asking them what the correct value of $((-1)^{2/3})^{3/2}$ is. This is on the assumption that you follow the convention that $x^{2/3}$ is equal to the square of the cube root of $x$ for all real numbers $x$.

But perhaps instead I should argue that $1$ must be equal to $\pm \mathrm{i}$, on the grounds that $((-1)^2)^{1/4}$ should be equal to $(-1)^{1/2}$?

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