## HatSimulator Group Title 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? one year ago one year ago

1. hartnn Group Title

Area of rectangular (here pasture) = Length * Width

2. HatSimulator Group Title

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 Group Title

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

4. hartnn Group Title

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

5. HatSimulator Group Title

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

6. hartnn Group Title

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

7. HatSimulator Group Title

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

8. HatSimulator Group Title

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

9. hartnn Group Title

good!

10. HatSimulator Group Title

Okay, 1 more?

11. hartnn Group Title

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

12. HatSimulator Group Title

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

13. HatSimulator Group Title

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

14. hartnn Group Title

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

15. hartnn Group Title

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 Group Title

okay

17. HatSimulator Group Title

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

18. hartnn Group Title

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

19. HatSimulator Group Title

Here you go

20. hartnn Group Title

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 Group Title

Oh man. So confused

22. HatSimulator Group Title

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

23. hartnn Group Title

yes.

24. HatSimulator Group Title

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

25. HatSimulator Group Title

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

26. hartnn Group Title

|dw:1360891677558:dw|

27. hartnn Group Title

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

28. hartnn Group Title

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

29. HatSimulator Group Title

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

30. HatSimulator Group Title

Howd 4 and the 4 more exponents come from

31. hartnn Group Title

32. hartnn Group Title

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 Group Title

OHHHHHHHHHHHHHHHHHH

34. HatSimulator Group Title

Yes, yes, go on (:

35. hartnn Group Title

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 Group Title

|dw:1360892393038:dw|

37. hartnn Group Title

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 Group Title

64

39. hartnn Group Title

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

40. HatSimulator Group Title

|dw:1360892627948:dw|

41. hartnn Group Title

12? how ?

42. HatSimulator Group Title

Wait

43. HatSimulator Group Title

|dw:1360892663950:dw|

44. HatSimulator Group Title

y^1*2

45. hartnn Group Title

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 Group Title

(y^2)

47. hartnn Group Title

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

48. HatSimulator Group Title

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

49. hartnn Group Title

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

50. hartnn Group Title

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

51. HatSimulator Group Title

No, i got it so far.

52. hartnn Group Title

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 Group Title

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

54. HatSimulator Group Title

55. hartnn Group Title

wow! thats absolutely correct! :)

56. hartnn Group Title

did you get how ?

57. HatSimulator Group Title

Yep!

58. HatSimulator Group Title

I get it now

59. HatSimulator Group Title

Thank you very much!

60. hartnn Group Title

welcome ^_^