Name:___________________________ Period:_________ Date:_______________ Negative Exponents and Exponents with Negative Bases Answers Section I. Explain the difference using sentences or math. !
!!
1. (−4) !"# 4 2. (−2)! !"# 2!! !
−4 !" !"!"#$%&'( !" −4 ∙ −4 ∙ −4 −2 ! !" !"#$%&'!() !" 1
1
−2 ∙ −2 ∙ −2 ∙ −2 ∙ −2 ∙ −2 4!! !" !"#$%&'!() !" ! !" 4
4∙4∙4
1
1
!!
2
!" !"#$%&'!() !" !" 2!
2∙2∙2∙2∙2∙2
!
!
3. (−3) !"# − 3 4. 7!! !"# (−7)! !
1
1
−3 !" !"#$%&'!() !" 7!! !" !"#$%&'!() !" ! !" 7
7∙7
−3 ∙ −3 ∙ −3 ∙ −3 → 81 −7 ! !" !"#$%&'!() !" −7 ∙ −7 −3! !" !"#$%&'!() !" − 3 ∙ 3 ∙ 3 ∙ 3 → −81 Section II. Write in exponential format (no fractions) !
!
!
7. 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 = 3 8. ! ∙! ∙! ∙! ∙! ∙! ∙! = !! 9. (−8) ∙ (−8) ∙ (−8) ∙ (−8) ∙ (−8) = −8 ! !
!
10. ! ∙! ∙! ∙! ∙! = !! !
!
11. ! ∙! ∙! ∙! = !! 12. −5 ∙ −5 ∙ (−5) ∙ (−5) = −5 ! !
!
14. ! ∙ ! ∙ ! = !! 13. 7 ∙ 7 ∙ 7 = 7! Section III. Solve 15. 8! = 64 18. (−2)! = −32 !
21. 3!! = !" 24. 4! = 64 27. −13! = −169 !!
30. −25!! = !"# 16. (−8)! = 64 !
19. 2!! = !" 22. −3! = −81 25. (−4)! = −64 28. −13 ! = −169 31. −25
!!
!
= !"# !
17. 8!! = !" 20. 2! = 32 23. (−3)! = 81 !
26. 4!! = !" !
29. −13 !! = !"# 32. −25 ! = 625