Intuition behind why 2^-1 is 1\2

^ symbol means exponent

What is 2^3 ? It is 8.
What is 2^2 ? It is 4.
What is 2^1? It is 2.

So, we can observe, that, as the exponent decreases from 3 -> 2 -> 1, each result is obtained by dividing by 2 – 8, 4 (8\2), 2 (4\2).

So, what is 2^0? Divide 2\2. And, the answer is 1 !!.

And, so what is 2^-1 ? Divide 1\2.!!

I learned this at Khan Academy

Another way of looking at negative exponents is,

A negative exponent means how many times to divide by the number.