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(3^9 – 3^8) (3^7 – 3^6) =

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(3^9 – 3^8) (3^7 – 3^6) =

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 × 3^14
(E) 4 × 3^14


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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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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)
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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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