Positive and Negative Exponents

Question

I know this is very basic but I’ve never been able to wrap my head around them. Please help. 😀

In: 4

Answer 1

Start with 1. By definition this is the zero exponent of all non zero numbers. Let’s use A to denote the base.

A^0 = 1

A^1 = 1 * A (multiply by one A)

A^2 = 1 * A * A (multiply by two A’s)

A^3 = 1 * A * A * A (and so forth)

A^(-1) = 1 / A (divide by one A)

A^(-2) = (1/A)/A = 1/(A*A) (divide by two A’s)

A^(-3) = ((1/A)/A)/A) = 1/ (A*A*A) (divide by three A)