OG Problem Solving Question #11

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acrowson: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Mon Dec 28, 2009 10:36 am

by acrowson » Wed Feb 03, 2010 12:52 pm

Hey guys,
I am trying to figure out the solution (pg. 191) for question #11 in the problem solving section.

Specifically, how the heck do I get from cube root (10^-6) to 10^-2??

Any help would be appreciated!

Thanks,
Andrew

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Source: Beat The GMAT — Problem Solving | Wed Feb 03, 2010 12:52 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Feb 05, 2010 8:10 am

acrowson wrote:Hey guys,
I am trying to figure out the solution (pg. 191) for question #11 in the problem solving section.

Specifically, how the heck do I get from cube root (10^-6) to 10^-2??

Any help would be appreciated!

Thanks,
Andrew

The important concept here is that cuberootx = x^(1/3)
In fact, the nth root of x is equal to x^(1/n)

So, cuberoot(10^-6) = (10^-6)^(1/3)
Applying the Power of a Power Rule, we multiply the exponents to get (10^-6)^(1/3) = 10^(-2)

Brent Hanneson - Creator of GMATPrepNow.com

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Fri Feb 05, 2010 9:05 am

acrowson wrote:
Hey guys,
I am trying to figure out the solution (pg. 191) for question #11 in the problem solving section.

Specifically, how the heck do I get from cube root (10^-6) to 10^-2??

Any help would be appreciated!

Thanks,
Andrew

its very simple as illustrated by, Brent Hanneson:
you can also understand it in a different way as below:
we can write 10^-6 = 1/10^6
cube root of 10^-6 = (10^-6)^(1/3) = (1/10^6)^(1/3) = 1/((10^6)^(1/3) ) -----(i)

now as u had confusion in calculating cube root of 10^-6 which is either way possible..
so I had simplified to a term which contains cube root of 10^6. Now I think u understand that cube root of 10^6 = 10^2

so from (i) cube root of 10^-6 = 1/((10^6)^(1/3) ) = 1/10^2 = 10^-2

I hope you also understand how 1/10^2 = 10^-2.

Well for clearing your concept completely you should refer a book of algebra , chapter power and indices. you can easily understand the concept.

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acrowson: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Mon Dec 28, 2009 10:36 am

by acrowson » Fri Feb 05, 2010 9:42 am

Thanks guys for the help...

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