Question

Complete the explanation for why 2−3 is the same as 1 23 . Look at the pattern below. As the exponent goes down by , the value is of what it was before. 23 = 8, 22 = 4, 21 = 2, 20 = 1, x−x = 1 2 , x−x = 1 4 , x−x = 1 8 = 1 23

Answer 1

`2^(-3)` is the same as
`(1)/(2^3)` because of the rule
`x^(-k) = (1)/(x^k)`

The negative exponent says to take the reciprocal of the base to make the exponent positive. The original base is 2, of which the reciprocal is 1/2.