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 $\frac{1}{2^3}$ because of the rule $x^{-k} = \frac{1}{x^k}$

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.