Simplifying GMAT Exponent Questions

by on August 28th, 2015

OLYMPUS DIGITAL CAMERAConsider the following example: 2^8 * 4^6 * 3^20

On the GMAT it is important to identify the difference between the base and the exponent. The bases in the above example are the 2, 3 and 4. The exponents are the 6, 8 and 20. A basic rule is to make the bases the same or make the exponents the same. If I had to choose, I’d rather make the bases the same, as the question usually becomes easier this way.

1. How to make the bases the same

  • You will notice that 4 is a multiple of 2. Let’s work with that. 4 can be expressed at 2^2. Thus, 4^6 becomes (2^2)^6 = 2^12.
  • The example can now be rewritten as 2^8 * 2^12 * 3^20. We have two bases that are the same.
  • In this case, you can add the exponents. 2^8 * 2^12 becomes 2^20. In algebraic terms, y^a * y^b = y^(a+b). The example becomes 2^20 * 3^20. You will notice that the exponents are the same. When this happens, the bases can be multiplied. In algebraic terms, y^a * z^a = (y*z)^a. 2^20 * 3^20becomes 6^20.

2. Simplifying expressions involving exponents

Consider another example:

Simplify (3^20 - 3^19)/2

Take the common factor in the numerator. This is 3^19. The expression thus becomes:

(3^19 (3-1))/2

= {3^19 * 2} / 2

= 3^19

3. The Division Rule

Consider: 2^5/2^3. The rule for dividing when the bases are same is that the exponent in the denominator can be subtracted from the exponent in the numerator. Or, in algebraic terms, x^a / x^b = x^(a-b). As such, 2^5/2^3 can be simplified to 2^2. In the heat of the moment during a test it can be difficult to remember all of the formulas involving exponents. You may be faced with a question that involves large numbers. If this happens, just take a simple example that you know is true. For example, 2^2 * 3^2 = 6^2. Thus, you can deduce the rule that when bases are different, but the exponents are the same, you can just multiply the bases and keep the exponent the same.

This post appeared first on the Economist GMAT Tutor blog.

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