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Hello good people!!!..Juriemagic here. First of all to all of you guys out there, sitting ready to help those in need, I wish each and every one a very happy and blessed 2016!...

I need some help with this problem please:

((p^2q)^3(2p^3q^-4)^2) / p^2q^3 * (4p^-2q^5)^3

 Jan 22, 2016

Best Answer 

 #5
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+5

(p2q)3(2p3qβˆ’4)2p2q3βˆ—(4pβˆ’2q5)3

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 Jan 22, 2016
 #1
avatar+4084 
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I'm ready to help with problems written in English,JK! I'm sorry, I can't help uπŸ˜₯

 Jan 22, 2016
 #2
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+5

Simplify the following:
((p^2 q)^3 ((2 p^3)/q^4)^2)/(p^2 q^3 ((4 q^5)/p^2)^3)

Multiply each exponent in p^2 q by 3:
(p^(3Γ—2) q^3 ((2 p^3)/q^4)^2)/(p^2 q^3 ((4 q^5)/p^2)^3)

3Γ—2  =  6:
(p^6 q^3 ((2 p^3)/q^4)^2)/(p^2 q^3 ((4 q^5)/p^2)^3)

Multiply each exponent in (2 p^3)/q^4 by 2:
(p^6 q^3Γ—(2^2 p^(2Γ—3))/((q^4)^2))/(p^2 q^3 ((4 q^5)/p^2)^3)

2Γ—3  =  6:
(2^2 p^6 q^3 p^6)/((q^4)^2 p^2 q^3 ((4 q^5)/p^2)^3)

2^2 = 4:
(4 p^6 q^3 p^6)/((q^4)^2 p^2 q^3 ((4 q^5)/p^2)^3)

Multiply exponents. (q^4)^2 = q^(4Γ—2):
(4 p^6 q^3 p^6)/(q^(4Γ—2) p^2 q^3 ((4 q^5)/p^2)^3)

4Γ—2  =  8:
(4 p^6 q^3 p^6)/(q^8 p^2 q^3 ((4 q^5)/p^2)^3)

Multiply each exponent in (4 q^5)/p^2 by 3:
(4 p^6 q^3 p^6)/(q^8 p^2 q^3Γ—(4^3 q^(3Γ—5))/((p^2)^3))

3Γ—5  =  15:
(4 p^6 q^3 p^6)/(q^8Γ—(4^3 p^2 q^3 q^15)/(p^2)^3)

Multiply exponents. (p^2)^3 = p^(2Γ—3):
(4 p^6 q^3 p^6)/(q^8Γ—(4^3 p^2 q^3 q^15)/p^(2Γ—3))

2Γ—3  =  6:
(4 p^6 q^3 p^6)/(q^8Γ—(4^3 p^2 q^3 q^15)/p^6)

4^3 = 4Γ—4^2:
(4 p^6 q^3 p^6)/(q^8Γ—(4Γ—4^2 p^2 q^3 q^15)/p^6)

4^2 = 16:
(4 p^6 q^3 p^6)/(q^8Γ—(4Γ—16 p^2 q^3 q^15)/p^6)

4Γ—16  =  64:
(4 p^6 q^3 p^6)/(q^8Γ—(64 p^2 q^3 q^15)/p^6)

(p^6 q^3Γ—4 p^6)/(q^8 (p^2 q^3Γ—64 q^15)/p^6) = q^3/q^3Γ—((p^6Γ—4 p^6)/q^8)/((p^2Γ—64 q^15)/p^6) = ((p^6Γ—4 p^6)/q^8)/((p^2Γ—64 q^15)/p^6):
((4 p^6 p^6)/q^8)/((64 p^2 q^15)/p^6)

Combine powers. (p^6Γ—4 p^6)/(q^8 (p^2Γ—64 q^15)/p^6) = (p^(6+6-2) 4 p^6)/(q^8Γ—64 q^15):
(4 p^6+6-2 p^6)/(64 q^8 q^15)

6+6-2 = 10:
(4 p^10 p^6)/(64 q^8 q^15)


4 | 1 | 6
| 6 | 4
- | 4 |
| 2 | 4
- | 2 | 4
|  | 0:
(p^10 p^6)/(16 q^8 q^15)

Combine powers. (p^10 p^6)/(16 q^8 q^15) = (p^(10+6) q^(-8-15))/16:
(p^10+6 q^-8-15)/16

10+6 = 16:
(p^16 q^(-8-15))/16

-8-15 = -23:
Answer: | (p^16 q^-23)/16

 Jan 22, 2016
 #3
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+5

((p^2q)^3(2p^3q^-4)^2) / p^2q^3 * (4p^-2q^5)^3

 

This is your question - is it what you intended or do you need more brackets?

 

(p2q)3(2p3qβˆ’4)2p2Γ—q3βˆ—(4pβˆ’2q5)3

 Jan 22, 2016
 #4
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+5

The intention is everything to the left of the division sign is on top, and everything right from it, at the bottom...

 Jan 22, 2016
 #5
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+5
Best Answer

(p2q)3(2p3qβˆ’4)2p2q3βˆ—(4pβˆ’2q5)3

Guest Jan 22, 2016
 #6
avatar+118696 
+5

Hi Juriemagic,

I see you still cannot log on    sad

 

(p2q)3(2p3qβˆ’4)2p2q3βˆ—(4pβˆ’2q5)3 =p6q3(22p6qβˆ’8)p2q3βˆ—(43pβˆ’6q15) =p6(4p6qβˆ’8)p2βˆ—(64pβˆ’6q15) =p4(4p6qβˆ’8)(64pβˆ’6q15) =4p4p6qβˆ’864pβˆ’6q15 =p10qβˆ’816pβˆ’6q15 =p10p+616q15q+8 =p1616q23

 

If you do not understand or you want a particular line discussed then please ask :)

 Jan 22, 2016
 #7
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0

Hi Melody!,

 

Thank you sooo much. I managed to do this sum but only to a point...

Yes, the logging on is still a problem, aw well, I'll speak with I.T. here and see if they can help...otherwise?..I trust you are all okay?

 Jan 22, 2016
 #8
avatar+118696 
0

Hi Juriemagic,

Admin knows that you and others have log in problems.  He does know how to fix it.

Have you tried using a different browser?  

 

 

Do you completely understand my answer?

You should thank guest answerer too.  He/she put in a lot of work on your behalf.   :/

 

 

Here are some more examples to practic on if you want

http://web2.0calc.com/questions/indices-especially-negative-indices

 Jan 22, 2016

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