Simplifying GMAT Exponent Questions
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 . Thus, becomes .
- The example can now be rewritten as . We have two bases that are the same.
- In this case, you can add the exponents. becomes . In algebraic terms, . The example becomes . You will notice that the exponents are the same. When this happens, the bases can be multiplied. In algebraic terms, . becomes .
2. Simplifying expressions involving exponents
Consider another example:
Take the common factor in the numerator. This is . The expression thus becomes:
3. The Division Rule
Consider: . 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, . As such, can be simplified to . 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, . 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.
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