Why can't I compute $(-2)^\frac28$ using a calculator?
2026-03-28 01:35:36.1774661736
Why can't I compute $(-2)^\frac28$ using a calculator?
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In Real Analysis, $$\left[(-2)^2\right]^{(1/8)} \tag1 $$
is not equal to (for example)
$$\left[(-2)\right]^{(1/4)} \tag2 $$
or
$$\left[(-2)^{(1/8)}\right]^2. \tag3 $$
In Real Analysis, despite the fact that the expression in (1) above is well defined, the expressions in both (2) above and (3) above are undefined.
Similarly, $\sqrt{-1}$ is undefined in Real Analysis.