(Calculator type: Sharp EL-W531)
When I put in the power (-0.2)^(-4/5) it says "calculation error."
Is this not just raising $(-0.2)^{-4}$ then taking the 5th root of that?
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@JoséCarlosSantos so I should first raise (-0.2)^-4 power, which I get 625 from. Then I take the 5th root of that and get approx 3.62. Is this right? Because if it is I'm not sure why the calculator can't compute that. – photon Apr 15 '22 at 08:31
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3The calculator isn't as clever as you think and it is erring on the side of caution when it comes to fractional roots of negative numbers. My calculator gives an error if I try to raise a negative number to anthing other than the power $\pm\frac 1n$ for an integer $n$. So I can do $(-0.2)^{\frac13}$ but not $(-0.2)^{\frac23}$. I imagine that yours is similar. – Peter Phipps Apr 15 '22 at 10:47
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1I cannot say for sure for your model, but in general when you calculate non-integer powers, a calculator computes it as $a^b = \text{exp}(b\cdot \log a)$. If $a \le 0$, then $\log a$ does not exist, so it generates an error. It is possible your model may do something different for fractional powers, but if so, it still doesn't like negative bases. – Paul Sinclair Apr 16 '22 at 02:52