## anonymous one year ago Is the answer B? I have to simplify. PICTURE BELOW WILL MEDAL :)

1. anonymous

2. UsukiDoll

yes it is B

3. anonymous

wait can you stay for more?

4. UsukiDoll

depends on the question...if it's easy... no problem

5. anonymous

6. anonymous

this is kinda tricky I think its A or B im not sure

7. UsukiDoll

well we need the exponent laws for $\frac{a^m}{a^n} \rightarrow a^{m-n}$ take it one at a time. for example if we have a = y, m = 5 and n = 3, we have $\frac{y^5}{y^3} \rightarrow y^{5-3}$

8. UsukiDoll

what is 5-3?

9. anonymous

2

10. UsukiDoll

yes so you have $y^2$. Now do the same thing for the z exponent

11. anonymous

z6

12. anonymous

Z^6

13. UsukiDoll

yes so your answer is $y^2z^6$

14. anonymous

why isn't a fraction?

15. anonymous

why isnt it a fraction*

16. UsukiDoll

we have positive exponents, so there's no denominator... if you have a negative exponent like $a^{-n} \rightarrow \frac{1}{a^n}$ then we need to rewrite it. Negative exponents are usually not allowed.

17. anonymous

thats how the next one looks hold up Im going to post it

18. UsukiDoll

ok.. A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side.

19. UsukiDoll

I just use the elevator rule.. whenever the negative exponent is on the numerator it goes down to the denominator... when there is a negative exponent on the denominator it goes up to the numerator.

20. anonymous

21. anonymous

my teacher said there shouldnt be any negative exponent in my final answer

22. UsukiDoll

$\frac{a^m}{a^n} \rightarrow a^{m-n}$ only this time we have a y = x, m = -5, and n = 9 so we have $\frac{x^{-5}}{x^9} \rightarrow x^{-5-9}$ so what is -5-9 ?

23. anonymous

-14

24. UsukiDoll

yes but due to the fact that negative exponents aren't allowed we need to rewrite is as $\frac{1}{x^{14}}$ We define a number with a negative exponent $a^{-n} = \frac{1}{a^n}$ It is the reciprocal of that number with a positive exponent The $a^{-n}$ is the reciprocal of $a^n$

25. anonymous

I'm going to post the last 4, im going to answer the next one tell me if im wrong

26. anonymous

27. anonymous

is it A?

28. UsukiDoll

no

29. anonymous

its B

30. UsukiDoll

$\frac{a^m}{a^n} \rightarrow a^{m-n}$ (exponent law) a = b, m =-2 n = -6. what's -2-6 ?

31. UsukiDoll

wait hold on.. I messed up . x.x

32. UsukiDoll

-2-(-6)

33. anonymous

4 lol

34. UsukiDoll

first one was right sorry sorry ^^

35. anonymous

oh I got it right?

36. anonymous

its A?

37. UsukiDoll

yeah because I neglected something

38. anonymous

39. anonymous

heres where it gets harder 2 more after this one by the way

40. UsukiDoll

weeeeee distributing exponents...

41. UsukiDoll

it's either write the whole fraction 7 times and add the exponents one by one or just distribute the exponent on x and y which is must faster

42. anonymous

so its D?

43. UsukiDoll

it's like we have x or x to the first power... $(x^1)^7 \rightarrow (x^{(1)(7)})$ yes it is

44. anonymous

it is D or no?

45. UsukiDoll

it's D

46. anonymous

okay 1 more after this one :)

47. anonymous

48. anonymous

is it B?

49. UsukiDoll

no.. because you are distributing the 5 distribution is multiplication . the 3 and the z portion is right for B but not x

50. anonymous

so its A because of 2 times 5?

51. anonymous

??

52. UsukiDoll

oh yeah... sorry I was trying to prove something to another user... it is A because you are distributing the exponent 5 all over the entire problem so you should have 3^5 x^(2)(5)/z^5

53. UsukiDoll

and 2 x 5 = 10

54. anonymous

heres the last one

55. anonymous

56. UsukiDoll

I'll give a hint: all of them switch places thanks to the distribution of the negative. whatever is on the numerator goes to the denominator and whatever is on the denominator goes on the numerator.

57. anonymous

D?

58. UsukiDoll

no... the -4 wasn't distributed on the 3 and when you have a problem like this you need to distribute everything.. all the numbers and variables have that distribution .

59. anonymous

okay

60. anonymous

C?

61. UsukiDoll

yes

62. anonymous

thank you so so much, are you going to be online still in like 8min?

63. UsukiDoll

because of the -4 which is already a negative exponent 3^(-4)x^(-4) goes down and y^(-4) goes up

64. UsukiDoll

I think I should still be there... on os

65. anonymous

theres another math homework I need help with so ill get back to you in a bit :) thank you by the way

66. UsukiDoll

ok :)