## anonymous 3 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. anonymous

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. anonymous

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. anonymous

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. anonymous

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

8. anonymous

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

9. hartnn

good!

10. anonymous

Okay, 1 more?

11. hartnn

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

12. anonymous

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

13. anonymous

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. anonymous

okay

17. anonymous

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. anonymous

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. anonymous

Oh man. So confused

22. anonymous

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

23. hartnn

yes.

24. anonymous

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

25. anonymous

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. anonymous

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

30. anonymous

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. anonymous

OHHHHHHHHHHHHHHHHHH

34. anonymous

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. anonymous

|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. anonymous

64

39. hartnn

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

40. anonymous

|dw:1360892627948:dw|

41. hartnn

12? how ?

42. anonymous

Wait

43. anonymous

|dw:1360892663950:dw|

44. anonymous

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. anonymous

(y^2)

47. hartnn

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

48. anonymous

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. anonymous

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. anonymous

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

54. anonymous

55. hartnn

wow! thats absolutely correct! :)

56. hartnn

did you get how ?

57. anonymous

Yep!

58. anonymous

I get it now

59. anonymous

Thank you very much!

60. hartnn

welcome ^_^