How would you explain 2^-3

Answer 1

The way I like to explain a negative exponent is that it changes the location and loses the negative. So if you have 2^-3, then 2 is technically in the numerator because 2/1 is 2.

Always take care of the negative exponent first. So since the 2^-3 is in the numerator, you flip the location to the denominator and lose the negative. Giving you 1/(2^3). Then evaluate the 2^3, which is 8. So the final answer would be 1/8.

One thing is to remember the negative does not change it from a positive to a negative number, just changed location from either the numerator (top) to the denominator (bottom) or the other way.

Answer 2

The negative exponent simply means that we have the number 1/(2^3)=1/8. In general, x^(-n)=1/(x^n).