(3^9 â€“ 3^8) (3^7 â€“ 3^6) =

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Sep 15, 2010 3:16 am

(3^9 - 3^8) (3^7 - 3^6) =
(A) 3^4
(B) 3^14
(C) 6^14
(D) 2 Ã— 3^14
(E) 4 Ã— 3^14

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Source: Beat The GMAT — Problem Solving | Wed Sep 15, 2010 3:16 am

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Wed Sep 15, 2010 4:55 am

(3^9 - 3^8) (3^7 - 3^6) = 3^8 (3 - 1) * 3^6(3 - 1) = 3^14 * 4

The correct answer is [spoiler](E)[/spoiler].

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Brian@VeritasPrep: GMAT Instructor; Posts: 1031; Joined: Thu Jul 03, 2008 1:23 pmFollowed by: 255 members; Location: Malibu, CA; Thanked: 716 times; GMAT Score:750

by Brian@VeritasPrep » Wed Sep 15, 2010 8:15 am

Hey everyone:

Rahul is dead on, but just in reading the subject line here I was reminded of a point I've made on here a lot lately. With exponents all of the rules that we know are related to multiplication/division and not addition/subtraction. It's tempting to want to just add or subtract here, but we don't have any rules that will help us do so with such large numbers.

When you see addition/subtraction in exponential problems, you'll almost always have to:

1) Factor to set up multiplication
2) Use the exponent rules for multiplication of same bases
3) Simplify, answer correctly, score 750, enroll at Stanford GSB

(3rd step optional, but recommended)

Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep

Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.

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Chirawat Sungkamee: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sun Aug 19, 2012 11:28 pm

by Chirawat Sungkamee » Sun Aug 19, 2012 11:50 pm

SOLUTION IN DETAIL:

Due to x^a * x^b = x^a+b, therefore

(3^9 - 3^8)(3^7 - 3^6) = (3^8 * 3^1 - 3^8)(3^6 * 3^1 - 3^6)
= (3^8 * 3 - 3^8)(3^6 * 3 - 3^6)
= {3^8(3-1)}{3^6(3-1)}
= 3^8 * 2 * 3^6 * 2
= 2 * 2 * 3^8 * 3^6
= 4 * 3^8+6
= 4 * 3^14
The answer is (E).

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