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)

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).