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# GMAT Tip: Exponent Manipulation – Tough questions, basic approaches

Today’s GMAT tip comes from Kaplan. In this article, Kaplan GMAT instructor Bret Ruber explains how to tackle tricky quantitative problems involving exponents:

Exponents questions are common among advanced quantitative problems and generally fall into two categories, both of which involve a variable in the exponent.

First are problems that ask test-takers to solve for an unknown in the exponent.  For example, the GMAT could tell you that 3x+1 = 272x-4, and ask you to solve for x.  The key strategy for a question such as this one is to set the bases equal to each other.  In this case, 27 can be written as 33, making our equation 3x+1 = (33)2x-4.  Make sure you know your exponent rules, because you are going to need them on the next step.  Specifically, you need to remember that (ab)c = abc.  Therefore, our equation becomes 3x+1 = 36x-12 once we distribute the 3.  Now that we have made our bases equal, we know that our exponents must also be equal.  Thus, x + 1 = 6x – 12.  From here we solve for x as with any other algebraic equation.

Second are problems that ask you to simplify an algebraic expression, again making that expression part of an exponent.  For example, the GMAT could give you the expression 4x + 4x + 2 and ask you to simplify.  Again, the key is remembering your exponent rules.  Because ab x ac = ab+c, we can write 4x + 2 as 4x x 42.  Now our equations reads as 4x + 42(4x).  Next we factor out the 4x, giving us 4x(1+42) = 4x(1+16) = 4x(17), which is how the answer would most likely be listed.

Whenever exponent problems in the two above categories appear, always make sure to make the bases the same and keep the exponent rules in mind.  By doing so, you can ensure your best chance of getting to the right answer in a timely fashion.