Exponent Time (GPREP)

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zagcollins: Master | Next Rank: 500 Posts; Posts: 167; Joined: Wed Jun 11, 2008 10:58 pm; Thanked: 2 times; Followed by:1 members

Exponent Time (GPREP)

by zagcollins » Wed Jul 30, 2008 4:22 am

( 8 )^2 (3)^3 (2)^4/96^2

Cant rem the answer options....can sum1 pls post a detailed explanation? i get totally confused halfway thru with all exponents sums..

Last edited by zagcollins on Wed Jul 30, 2008 5:08 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Wed Jul 30, 2008 4:22 am

Karthik12: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Sun Jul 20, 2008 10:36 pm

by Karthik12 » Wed Jul 30, 2008 4:27 am

Ans is 3

Hopes its correct

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pm; Location: INDIA; Thanked: 84 times; Followed by:3 members

by sudhir3127 » Wed Jul 30, 2008 7:17 am

My answer 3.

here it goes..

((8^2) * (3^3) * (2^4)) / (96^2)

8^2 can be written as (2^3)^2
96^2 can be written as (16.6)^2 ..this further can be written as
(2^4)2* 6^2

((2^3)^2*(3^3) * (2^4))/ (2^4)2* 6^2

2^6*27*2^4/(2^8* 6^2)

27*4/36= 3

hopes this is clear

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malolakrupa: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Fri Jul 18, 2008 12:26 pm; Thanked: 2 times

by malolakrupa » Wed Jul 30, 2008 7:21 am

This can be simplified as A / B

A can be simplified to (2^3)^2 * 3^3 * 2^4
and B can be simplified to 3^2 * 2^10

Hence A / B gives 3

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zagcollins: Master | Next Rank: 500 Posts; Posts: 167; Joined: Wed Jun 11, 2008 10:58 pm; Thanked: 2 times; Followed by:1 members

by zagcollins » Wed Jul 30, 2008 9:18 am

what i need to understand here is how to simplify a number like 96^2 during the examination...

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preetha_85: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Sun Jul 06, 2008 6:41 am; Location: INDIA; Thanked: 2 times

by preetha_85 » Wed Jul 30, 2008 10:28 am

Hi

Since we have 8 nd 2 in the numerator try to split 96 into multiples of 8 nd 2 so tat we cancel out the common factors...

Hope this helps..

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fajoni: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Mon Mar 10, 2008 1:13 pm; Thanked: 2 times

by fajoni » Wed Jul 30, 2008 5:03 pm

Here is an example of a general rule when one is dealing with large numbers that are raised to the nth power:

12^2 is the same thing as 3^2 times 4^2 or 6^2 times 2^2. In general, a large number raised to a power is equal to the factors of that number raised to the same power. I hope you see how useful this can be on this question.

The easiest thing to do, IMHO, is break 96 into its factors and sqaure them. Start with 8, since 8 is the largest base number in the numerator:

96^2 = 12^2 times 8^2, thus, the 8's cancel each other out and you're left with (3^3 times 2^2)/12^2. Continue to break 12 down into it's factors and square them:

12^2 = 4^2 times 3^2, thus, all but one three is cancelled.

You now have 3(2^4)/4^2...

4^2 = 2^2 times 2^2, or 2^4

Thus, the two's cancel out and you're left with 3 as your answer.

I hope this helps. I apologize in advance if this post is difficult to follow.

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Vignesh.4384: Master | Next Rank: 500 Posts; Posts: 443; Joined: Sat Jun 28, 2008 6:33 pm; Thanked: 5 times

by Vignesh.4384 » Wed Jul 30, 2008 7:28 pm

HI zagcollins.

simplfying 96^2 should not be 2 difficult.

take this simple eg first 15^32.
split 15 into prime factors. which are 3 and 5

so 15^32 = (3^32) * (5^32). [after all 15^1 = (5^1) * (3^1)

]

coming to ur qestion .

96 = 2 * 2 * 2 * 2 * 2* 3 (simple factorization)
or
96 = (2 * 2 * 2) * (2 * 2)* 3 = 8 * 4 * 3

now we wil incorporate the power .
96 ^ 2 = (8^2) * (4^2) * (3^2).

96^2 is reduced to a form that is almost similar to the numerator.

now u just have 2 cancel the powers.

Regards,
Vignesh

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