[Tohopekaliga]

Exponents are a notation, and not something specifically intrinsic to numbers.

So, when you have 4^3, you’re shorthand writing 1 * 4 * 4 * 4.

Negative exponents are divisions, so 4^-3 is 1 / 4 / 4 / 4, which is the same as 1 / (4 * 4 * 4), or 1/(4^3).


It also might help to consider that 4^4 * 4*^-2 = 4^2, since 4-2 = 2, also that (4 * 4 * 4 * 4) / (4 * 4) = (4 * 4)