Negative Exponents with Powers of 10 and What about Other Bases?

Students extend the rules they have developed for working with powers to negative exponents. This video lesson presents negative powers of 10 as repeated multiplication by 1/10, leading ultimately to the rule . Students use repeated reasoning to generalize about negative exponents (MP8). They create viable arguments and critique the reasoning of others when comparing and contrasting, for example, (10^-2)³ and (10²)^-3 (MP3). Students also use their understanding of exponent rules with powers of 10 to make sense of exponent rules for powers of other bases. Students work through problems analogous to the ones used to develop exponent rules for powers of 10. The same underlying patterns emerge, revealing the fact that the exponent rules are the same for bases other than 10.

Grade 8, Episode 19: Unit 7, Lessons 5 & 6 | Illustrative Math