Back to my question supposing am alone evaulating this

\(\displaystyle \frac{ 1 }{( - 8 ) ^ {\frac{ - 1 }{ 3 }}} + \frac{ 1 }{( - 32 ) ^ {\frac{ - 1 }{ 5 }}} - \frac{ 1 }{( - 64 ) ^ {\frac{ - 1 }{ 3 }}}\)

How do check if the solution is correct at the end of the evaluation just like in the instances I gave?

Checking a

**simplification **is different from checking a

**solution **of an equation; but fortunately, this is a

**numerical expression**, so the obvious thing is just to type the whole thing into an algebraic calculator, or equivalent.

But that's a little more troublesome than I expected. I first typed

1/(-8)^(-1/3)+1/(-32)^(-1/5)-1/(-64)^(-1/3)

into Google, and got this:

Oops! It looks like they used complex roots. I've seen that happen before, there or on some calculators, because they handle exponents in funny ways.

Then I pasted the same expression into the Windows calculator, and got this:

I was confused for a while, but eventually realized that this is the value of just the last exponent I'd entered, because I didn't end it with "="; when I hit Enter after this, I got

This results from a rounding error somewhere. But it's interesting how it interpreted what I entered (for example, "-" is taken as subtraction, not negation, but it inserted 0 appropriately.

I tried again, entering everything by hand following the calculators rules (e.g. 1 divided by 8 negate ^ 3 negate reciprocal ...), and got the same final result.

Finally I pasted the same thing into Excel and got the right answer, 0. A physical calculator should do the same.

But these various errors are instructive!

Now, if you want to check without using technology, then the thing to do is to work it out again a different way.