Janu16 one year ago Which of the following are equivalent? Justify your reasoning Wait till i draw all the options

1. Janu16

|dw:1438040615062:dw|

2. Janu16

@DanJS

3. jim_thompson5910

What does choice B simplify to?

4. Janu16

x1?

5. jim_thompson5910

x^1 you mean? if so, then yes x^1 = x |dw:1438041275973:dw|

6. jim_thompson5910

7. Janu16

ya that

8. Janu16

how do you simplify tht? add?

9. jim_thompson5910

|dw:1438041368560:dw|

10. jim_thompson5910

Due to the rule $\LARGE x^a*x^b = x^{a+b}$

11. Janu16

|dw:1438041074473:dw|

12. jim_thompson5910

good

13. Janu16

wait 3x

14. jim_thompson5910

so C is not equal to A, and not equal to B

15. jim_thompson5910

no there's no 3x

16. Janu16

oh ok

17. jim_thompson5910

|dw:1438041475304:dw|

18. Janu16

ok i see

19. jim_thompson5910

now simplify D

20. Janu16

so you just add the top right so 3/3?

21. Janu16

is there 3x for this

22. jim_thompson5910

yeah 1/3+1/3+1/3 = (1+1+1)/3 = 3/3

23. jim_thompson5910

no 3x

24. jim_thompson5910

x*x = x^2 NOT x*x = 2x

25. Janu16

so x3/3 only?

26. jim_thompson5910

$\Large x^{1/3}*x^{1/3}*x^{1/3} = x^{1/3+1/3+1/3}$ $\Large x^{1/3}*x^{1/3}*x^{1/3} = x^{(1+1+1)/3}$ $\Large x^{1/3}*x^{1/3}*x^{1/3} = x^{3/3}$ $\Large x^{1/3}*x^{1/3}*x^{1/3} = x^{1}$ $\Large x^{1/3}*x^{1/3}*x^{1/3} = x$

27. jim_thompson5910

|dw:1438041705953:dw|

28. Janu16

so b and d are equivalent?

29. jim_thompson5910

correct

30. Janu16

so how do i justify the reasoing

31. Janu16

@jim_thompson5910

32. jim_thompson5910

You're simplifying each expression using the rule $\LARGE x^a*x^b = x^{a+b}$

33. jim_thompson5910

for part B, you also use the fact that $\Large \frac{1}{x^{-k}} = x^k$

34. Janu16

ok thanks!

35. jim_thompson5910

no problem

36. Janu16

i will just out it in words