January 8th, 2017, 05:49 AM  #1 
Member Joined: Nov 2016 From: Ireland Posts: 84 Thanks: 3  Simplify the monster
Ok so I woke up this morning to find this thing at the bottom of my bed. I've an exam tomorrow. This was from a previous paper. First bloody question on the exam. The poor critters. I had to take a pic because the thing was to hard to write Sorry I know it's a lil big. The picture I mean. Now then so I started by getting rid of them square roots. Ending up with just (c) on the numerator and b^2 on the bottom I was thinking to myself  Ok better distribute out the top part see what we've got. But that just ends up a proper mess. So I was thinking ok put them in brackets beside each other. (3a^1/2 x b^1 x c) (3a^1/2 x b^1 x c) Perhaps then I could use the powers on the bottom and just start subtracting away from the powers of the first term on the top...? Or maybe I need to multiply out the term using a common denominator. But then that ends up a mess as well. Can someone please push me in the general right direction. Thanks guys sorry I'm such a n00b. Last edited by Kevineamon; January 8th, 2017 at 06:34 AM. 
January 8th, 2017, 06:55 AM  #2 
Member Joined: Nov 2016 From: Ireland Posts: 84 Thanks: 3 
Had an idea. I was thinking using the power rule I could add up those powers in the two terms I've separated. Lets see hmmm (3a^1/2 x b^1 x c) (3a^1/2 x b^1 x c) 3a x 2b^2 x c^2 Hmmm is that right? Can I just do that? Would avoid the distribution 
January 8th, 2017, 07:02 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,296 Thanks: 934 
Got a headache as soon as I saw that ! Soooooo: http://www.wolframalpha.com/input/?i...4)*c%5E(1%2F3)) I entered: x=(3*sqrt(a)*b^(1)*sqrt(c^3))^2/(a^(7)*sqrt(b^4)*c^(1/3)) Last edited by Denis; January 8th, 2017 at 07:07 AM. 
January 8th, 2017, 07:06 AM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,122 Thanks: 1102 
$\Large \dfrac{\left(3a^{1/2}b^{1}\sqrt{c^3}\right)^2}{a^{7}\sqrt{b^4}c^{1/3}}=$ $\Large \dfrac{\left(3 a^{1/2} b^{1}c^{3/2}\right)^2}{a^{7}b^2 c^{1/3}}=$ $\Large \dfrac{9 a b^{2} c^3}{a^{7}b^2 c^{1/3}}=$ $\Large 9a^8 b^{4}c^{10/3} = $ $\Large \dfrac{9 a^8 c^{10/3}}{b^4}$ Last edited by romsek; January 8th, 2017 at 07:25 AM. 
January 8th, 2017, 07:12 AM  #5 
Senior Member Joined: May 2016 From: USA Posts: 1,148 Thanks: 479 
There really is no way to avoid the work, but there really is not that much if you use PEMDAS. $\dfrac{ \left ( 3a^{(1/2)}b^{1}\sqrt{c^3} \right )^2}{a^{7}\sqrt{b^4}c^{1/3}} =$ $\dfrac{9a b^{2} c^3}{a^{7} b^2 c^{1/3}} =$ $\dfrac{9a * a^7 * c^3 * \sqrt[3]{c}}{b^2 * b^2} =$ $what?$ 
January 8th, 2017, 07:14 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,296 Thanks: 934 
Romsek, in denominator: c^(1/3), not c^(1/3)

January 8th, 2017, 07:38 AM  #7 
Member Joined: Nov 2016 From: Ireland Posts: 84 Thanks: 3 
Thanks guys  interesting some of my ideas seemed to be correct, which shows my math brain is at least partially working. K let me stare at this thing for another while. Cheers guys you're the best 
January 8th, 2017, 08:01 AM  #8 
Member Joined: Nov 2016 From: Ireland Posts: 84 Thanks: 3 
Very interesting the way that $\displaystyle c^3/c^{1/3} became $ $\displaystyle c^{10/3} $ Never knew that very interesting  thanks again guys 
January 8th, 2017, 09:32 AM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,296 Thanks: 934 
Ya...tattoo this on your wrist: x^a / x^b = x^(ab) ; 3^7 / 3^4 = 3^(74) = 3^3 
January 8th, 2017, 10:09 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,296 Thanks: 934 
$\Large \dfrac{9 a^8 c^{10/3}}{b^4}$ Question: that of course implies that b<>0; will most teachers deduct a point or more if that's not specified as part of the answer? 

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