### Home > PC > Chapter 1 > Lesson 1.1.1 > Problem 1-8

2

^{6}=2

^{5}=2

^{4}= 162

^{3}= 82

^{2}= 42

^{1}= 22

^{0}=2

^{−1}=2

^{−2}=2

^{−3}=2

^{−4}=2

^{−}^{n}^{ }=REVIEW OF ZERO AND NEGATIVE EXPONENTS

Sarah was teaching her younger sister Tanya about exponents. Tanya thought that 2

^{0}= 0 and 2^{–1}= –2, but Sarah told her that was wrong. To help Tanya, Sarah made a table like the one shown at right and filled in the values shown. Homework Help ✎Sarah told Tanya that the numbers in the right column double each time as you go up. Explain why they are double by writing 2

^{2}, 2^{3}, and 2^{4}as products of 2’s.On your own paper, copy the table and fill in the values for 2

^{5}and 2^{6}.What happens to the values in the right column as we go down from 2

^{6}?In order to make the rules of exponents in base 2 work for all integer exponents, mathematicians

*define*2^{0}, 2^{−1}, etc. by using the pattern you saw in part (c). Use this pattern to fill in the remaining values in the right column.

2^{2} = 2·2

2^{3} = 2·2·2

2^{4} = 2·2·2·2

They are reduced by half.