Why is $-2-3(-1)^{2/3} = -5$? Have I gone mad? Consider this:

$$f(x) = -2-3x^{\frac {2}{3}}$$

Why would $f(-1) = -5$?

Doesn't make sense to me. $f(-1)$ equals $1$ when plugging it in on my calculator. But in my book and when plotting this using google's plot feature (just google this: "-2-3(x^(2/3))" and hover over $-1$), I get $f(-1) = -5$?
How do you define $(-1)^{2/3}$? That is the crux.
We can write  $-1^\frac23$ as $(-1^2)^\frac13$  which is equal to $\sqrt[3]1$ which is 1. So $-2 - 3(1) = -5$.

Note that it doesn't matter what you do first whether the cube root or the square. $\sqrt[3]{-1} = -1$ and ${(-1)}^2 = 1$. So you still get the same answer $-5$