## anonymous one year ago Im trying to solve this problem and my answer keep coming up in decimals. need help 2^6X2^-3/20^10/2-8

1. anonymous

$2^{6}\times2^{-3}\div2^{10}\div2^{-8}$

2. Nnesha

don't use calculator. you will not get decimal answer.

3. anonymous

I'm not which means I must be doing something wrong

4. Nnesha

ohh nvm then show your work please don't even touch the base just move around the exponents

5. Nnesha

exponent rule you can't have the negative exponent $x^{-m}=\frac{ 1 }{ x^m }$ flip the fraction to make it positive exponent

6. Nnesha

$\huge\rm \frac{ x^{-m} }{ 1 }=\frac{ 1 }{ x^m }$

7. anonymous

are we talking about an imaginary base under the entire problem ? sorry

8. Nnesha

imaginary base ??? :o

9. Nnesha

$\huge\rm \frac{ 2^6 \times 2^{-3} }{ \frac{ 2^{10} }{ 2^{-8}} }$ this is your question right where 2 is the base

10. anonymous

NO

11. anonymous

refer to the initial post showing the actual problem

12. Nnesha

$\huge\rm \frac{\color{reD}{ 2^6 \times 2^{-3}} }{ \frac{ 2^{10} }{ 2^{-8}} }$ solve the red part first when you multiply same bases you should add their exponents

13. anonymous

okay what about the division ? my results now come back to 1^1

14. Nnesha

alright $\rm \color{Red}{2^6 \times 2^{-3} }\div 2^{10} \div 2^{-8}$

15. anonymous

Yes

16. Nnesha

same thing. :=) solve the red part first

17. anonymous

okay than divide from left to right subtracting the exponents right?

18. anonymous

okay so my new answer is 4^{27}

19. anonymous

4^27

20. Nnesha

how did you get 4 ?

21. zzr0ck3r

there is nothing wrong with decimals

22. anonymous

2X2

23. Nnesha

just play with the exponents don't even touch the base

24. Nnesha

multiply the same u would add their exponents alright $\rm \color{Red}{2^{6+(-3)} }\div 2^{10} \div 2^{-8}$ like this

25. anonymous

So leave the base and add and subtract the exponents? new answer$2^{-36}$

26. anonymous

correction sorry wrong numbers

27. Nnesha

no.. i said when you multiply the same bases then u should add $\huge\rm \color{Red}{2^6 \color{blue}{\times }2^{-3} }\div 2^{10} \div 2^{-8}$ here are multiplying 2^6 times 2^{-3 that's why we should add the base

28. anonymous

29. Nnesha

$\huge\rm \color{black}{2^{6+(-3)} }\color{red}{\div} 2^{10} \color{red}{\div }2^{-8}$ different rule when you divide same bases $\rm \frac{ x^m }{ x^n }=x^{m-n}$

30. anonymous

okay so my results should be 2^-15

31. Nnesha

how did you get -15 ?

32. anonymous

okay I first did 6+-3= 3 than I did 10- -8= 18 3-18=-15?

33. Nnesha

thanks for showing your work much appreciated ! $\huge\rm \frac{ \color{ReD}{\frac{ 2^3 }{ 2^{10}}} }{ 2^{-8} }$ first solve the red part we should move the 10 to the top first and then

34. Nnesha

$\huge\rm \frac{ 2^{3+(-10)} }{ 2^{-8}}$ try to solve now!

35. anonymous

2^1? final answer, I did 3+-10= -7 than -7 - -8= 1 2^1

36. Nnesha

YAYAY!!

37. anonymous

Really I though I got it wrong waohh

38. anonymous

but how did we went from the original problem to this?

39. anonymous

final one?

40. Nnesha

we used two exponents rule! $\huge\rm \frac{ x^m }{ x^n }=x^{m-n}$ divide same base $\huge\rm x^m \times x^n = x^{m \times n}$ when you multiply same bsses

41. anonymous

holly cow for some reason I feel lost a bit. questions can you give a practice problem to solve for you.

42. Nnesha

sure sure $\huge\rm \frac{\frac{ 3^6 \times 3^7 }{ 3^4} }{ 3^{-5} }$

43. anonymous

give me a sec to resolve thanks

44. zzr0ck3r

I want to make one thing clear: you are of course allowed to have negative exponents it is just that your teacher wants to make sure you can go back and fourth.

45. Nnesha

so why we can't leave the negative exponent when it says simplify

46. Nnesha

:=)

47. Nnesha

actually sometimes we could , depends on the answer choices :P haha

48. anonymous

49. anonymous

thanks pinkiepug I will

50. anonymous

51. anonymous

okay here is my answer and problem|dw:1440395883759:dw|

52. Nnesha

uh-oh |dw:1440395977961:dw| mistake

53. anonymous

? humm

54. Nnesha

|dw:1440396028569:dw| move the 4 to the top when do you that sign would change $\frac{ x^m }{ x^{n} }=x^{m-n}$

55. anonymous

it should be 13-4 = 9

56. Nnesha

$$\huge\color{green}{\checkmark}$$

57. anonymous

than 9- (-5)= 14

58. anonymous

59. Nnesha

perfect! great job!

60. Nnesha

i'm sooooooooooooooo sleepy gtg bye! good luck!

61. anonymous

thank you so much have a good night and week

62. Nnesha

my pleasure /same to u!