The exception to this is when the power can be written as a fraction that has an odd denominator.

e.g -8^(1/3) = -2.

If you think about it, that applies to integer powers as well, it's just that the denominator in that case is 1!

Or 1. Same thing. =P

]]>In (-27)^(10/4) and (-27)^(5/2), I guess the first caculation done is the numerator of the exponent, then the root is extracted.

In the former, since after the number is raised to the numerator, a positive number is got, there's no problem for the calculator to perform the next calculation, that is extracting the 4th root. But in the latter, the 5th power of -27 is a negative number and the operation of square-root of a negative number cannot be performed, unless the calculator works with complex numbers/imaginary numbers.

The calculator in the scientific mode in the system I am now using says 'Invalid input for function' when I input -27^(5/2) or -27^(10/4). I am not aware whether the fraction mode, i.e a/b is available, for input. ]]>

Or maybe there are certain negative fractional powers that work...

Let's see 16^(-1/2) = 1/4, so that works with a negative fractional power, hmm.

I thought my calculator didn't like something.

Oh yeah, it was a fractional power of a negative number.

But this is sometimes okay. It all depends I guess.

Like (-27)^(1/3) = -3, so that works.

But (-27)^2.5 would probably fail.

Let's see. (-27)^(10/4), yeah that works, but (-27)^(5/2) doesn't work.

Anyone see the flaw?]]>

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a¹ is a

a² is a x a

a³ is a x a x a and so on.

It is a convention that any number raised to the power zero is 1,

since, the law of indices states that

When m and n are equal,

We know

Therefore, by convention,

]]>

a to the power of zero]]>