## HatSimulator 2 years ago A rectangular pasture has a fence around the perimeter. The length of the fence is 16x7 and the width is 48x4. What is the area of the pasture? (1 point) a) 3x^3 b)128x^11 c)768x^11 d)768x^28 I KNOW the answer is c, but i need it explained. I already found it here once but can ANYONE explain how to do this?

1. hartnn

Area of rectangular (here pasture) = Length * Width

2. HatSimulator

Allright, so how do i do it? 16 * ^7 gives nothing and im so confused How do i do 16x^7 * 48x^4? I dont get this problem

3. HatSimulator

Same thing with this > Simplify. 5^–1(3^–2) If i type this into a calculator i get a stupid number

4. hartnn

ok, treat constants and variables separately. $$16x^7 \times 48x^4 = (16\times 48) \times(x^7 \times x^4)$$ got this ?

5. HatSimulator

Okay... yes i think i get that... but where did the two Z come from

6. hartnn

Z ?? there are no Z's there....

7. HatSimulator

Whoops, sorry, okay, go on. I understand now

8. HatSimulator

I think i get it 16 * 48 = 768 And 7 + 4 = 11?

9. hartnn

good!

10. HatSimulator

Okay, 1 more?

11. hartnn

actually, its $$x^7 \times x^4 = x^{7+4}=x^{11}$$ and sure :)

12. HatSimulator

Okay something like this Simplify (4xy2)3(xy)5 and (sorry) this Evaluate a–4b2 for a = –2 and b = 4

13. HatSimulator

Simplify (4xy^2)^3(xy)^5 Sorry

14. hartnn

i believe the first one looks like this : $$(4xy^2)^3(xy)^5$$

15. hartnn

ok, so you need to remember/understand few thing before u start: $$\huge (ab)^n = a^nb^n$$ and $$\huge (a^m)^n=a^{mn}$$

16. HatSimulator

okay

17. HatSimulator

The other problem i can't figure out how to write an equation

18. hartnn

$$\large Evaluate \: \: a^{–4}b^2 \:\: for\:\: a = –2 \:\:and\:\: b = 4$$ right ?

19. HatSimulator

Here you go

20. hartnn

ok, for the previous one : using, $$\huge (ab)^n = a^nb^n$$ $$\large (4xy^2)^3= 4^3 x^3 (y^2)^3$$ got this ?

21. HatSimulator

Oh man. So confused

22. HatSimulator

Are you doing Simplify (4xy^2)^3(xy)^5 ?

23. hartnn

yes.

24. HatSimulator

And you changed that to (4xy^2)^3=4^3x^3(y^2)^3....

25. HatSimulator

How did you do that... that hurts my brain

26. hartnn

|dw:1360891677558:dw|

27. hartnn

open up your brain and try to accept new things :)

28. hartnn

basically the exponent outside the bracket becomes the exponent of each of the terms inside the bracket.

29. HatSimulator

Where did averything after that equal sign come from? Where'd the 5 go?

30. HatSimulator

Howd 4 and the 4 more exponents come from

31. hartnn

32. hartnn

if you are asking from where does all the exponents come from take a look at this again : $$(ab)^n=a^nb^n$$ or perhaps : $$(abc)^n=a^nb^nc^n$$

33. HatSimulator

OHHHHHHHHHHHHHHHHHH

34. HatSimulator

Yes, yes, go on (:

35. hartnn

so i assume you are clear with this diagram.|dw:1360892207194:dw| using same rule, can you tell me what u get for $$(xy)^5$$ ??

36. HatSimulator

|dw:1360892393038:dw|

37. hartnn

correct :) see, it isn't difficult at all. now you have $$\large 4^3x^3(y^2)^3x^5y^5$$ right ? lets start simplifying with constants (numbers) 4^3 =... ?

38. HatSimulator

64

39. hartnn

yes. now comes the 2nd rule i posted. $$\huge (a^m)^n=a^{mn}$$ so, what about $$(y^2)^3$$ ??

40. HatSimulator

|dw:1360892627948:dw|

41. hartnn

12? how ?

42. HatSimulator

Wait

43. HatSimulator

|dw:1360892663950:dw|

44. HatSimulator

y^1*2

45. hartnn

umm..no, let me give you an example $$\large (z^5)^3 = z^{5 \times 3 }=z^{15}$$ do similar thing for $$(y^2)^3$$

46. HatSimulator

(y^2)

47. hartnn

:O the exponents are getting multiplied. what are the 2 exponents in $$(y^2)^3$$

48. HatSimulator

Its a 3 isnt it... Sorry (y^6)

49. hartnn

yes, y^6 is correct. so, we have now $$64x^3y^6x^5y^5$$ lets bring 'x' terms and y terms together.

50. hartnn

$$64 \: \: (x^3x^5) \:\: (y^6y^5)$$ ok, any doubts ?

51. HatSimulator

No, i got it so far.

52. hartnn

now one of the very important rule : $$\large a^m a^n = a^{m+n}$$ here, if we multiply the variables, their exponents gets ADDED . so, what about $$x^3x^5=... ?$$

53. HatSimulator

It would end up being 64(x^8)(y^11) ?

54. HatSimulator

55. hartnn

wow! thats absolutely correct! :)

56. hartnn

did you get how ?

57. HatSimulator

Yep!

58. HatSimulator

I get it now

59. HatSimulator

Thank you very much!

60. hartnn

welcome ^_^