Exponent Challenge Question Series: Final Answer

by on October 1st, 2010

This is the last post in a series of five blog posts that we published this week highlighting challenging exponent questions!

This week on Beat The GMAT, Veritas Prep’s authors will each day contribute a difficult exponent-related challenge problem, with a solution to follow the next day. Before you begin, you may want to consider this as a way to crack the exponent code; nearly all exponent-based problems can be solved using a combination of these three guiding exponent principles:

  1. Exponent rules are almost all related to multiplication and division with virtually no rules that directly apply to addition and subtraction. When facing exponent problems, look for opportunities to factor and multiply to put yourself in a position to use your multiplication-heavy exponent expertise.
  2. Most exponent rules require you to have common bases in order to apply them, so look to break down bases into prime factors so that you have common bases with which to work.
  3. Exponents are very pattern-driven, so when large numbers are present you can often establish a rule using small numbers and then extrapolate it to the larger ones.

Yesterday’s Challenge Question and Solution

If you haven’t don’t so already, try out yesterday’s problem first before reviewing the solution.

If 3^{(x+2)}-3^{x}=6^{3}(3^{7}), what is the value of x?

(A) 10
(B) 11
(C) 12
(D) 13
(E) 14

A. Factoring the additive terms on the left hand side of the equation allows you to multiply with exponents which is almost always a good decision. Factoring out 3^x leaves: 3^{x}(3^{2}-1)=6^{3}(3^{7}). As with most exponent problems, you’ll also want to break out each base into prime factors so that you have common bases. 6^{3} can be written as(2*3)^{3}or 2^{3} * 3^{3} and the 8 that results from the parenthetical on the left (3^2-1) can also be written as 2^{3}, leaving:

3^{x}*2^{3}=2^{3}*3^{3}*3^{7}.

The 2^{3} terms factor, and the 3^{3}*3^{7} terms combine to 3^{10}.

Therefore, x = 10.

Read the entire Exponent Series here:

2 comments

  • excellent set of question covering exponents. i hope btg allows veritas to keep doing this for other topics etc

  • Wow! excellent question and nice solution. I s this 700+ question?

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