Table of Contents
- Exponents
- Radicals and Roots
- Exponent Rules
- Common Exponent Traps
- How to Approach Exponential Equations
- Powers of Numbers
Exponents
Exponents denotes the repeated multiplication of a quantity by itself
Radicals and Roots
Radicals and roots are used to denote numbers that are taken to fractional exponents. The square root of a number simply denotes that a number is taken to the ½ power. Radicals should always be converted to fraction form to simplify calculations
Common Roots
The following is a list of common roots tested on the GMAT. These roots need to be memorized.
Exponent Rules
The GMAT likes to test an individual’s knowledge of mathematical operators. Exponents are an especially popular topic. The key to solving most exponential equations is to understand the underlying rules that govern them; this will allow you to successfully manipulate the equations to find the right solution. The follow list needs to be memorized:
Common Exponent Traps
Even Term Exponents
Exponential equations with one term and an even power can have two or more solutions. Always break down an even exponent into two scenarios, one where the solution is positive and one where the solution is negative.
Example
Be particularly careful whenever you see even exponents because even exponents hide the sign of the base.
Example
x can equal 0, 1, -1
Odd Term Exponents
Exponential equations with one term and an odd power will have only one solution. The solution will always have the same sign as the original term.
Example
Multiple Term Exponents
Exponential equations with multiple terms and both even and odd exponents are basically polynomials and can have multiple solutions. Solution terms can vary from positive to negative, so each equation must be solved on a case by case basis.
Example
How to Approach Exponential Equations
The GMAT will often ask you to solve an exponential equation. The following technique can be used to quickly reduce exponents into simpler terms.
- Given our knowledge of exponential rules cited above, combine terms and see if any bases or exponents can be eliminated
- Factor out exponents, always starting with the smallest exponent first.
- Simplify constants and solve
Example
Powers of Numbers
The following table contains powers of numbers that are commonly tested on the GMAT. Memorize this list to reduce time spent on calculations.
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