About: Exponents, GMAT, Quantitative, Square Root
Exponents and Square roots are an integral part of the Quantitative section of the GMAT, a solid understanding of how they work will save you time and confusion on the test day.
Exponents
Here are the most important basics about Exponents:
Definition: An exponent is basically the little number that goes on top of another number. In 5² five is the “base” and 2 is the exponent. This means that 5² is 5 x 5 (25). 5³ is 5 x5 x5 (125).
Important properties of bases and exponents:
- If the base is positive, no matter what the power (exponent) is, will remain positive.
- If the base is negative, and the exponent is odd than the end result is still negative.
- If the base is negative, and the exponent is even than the end result becomes a positive number.
- Any term with an odd power that results in a negative number means that the base will be negative as well.
For example: a³ = -125 means that the base has to be negative for that to be possible. In this case “a” is -5.
- If the exponent is ² than there are always two possible bases can always be either positive or negative.
For example: a²=64 means that “a” could be either positive (+8) or negative (-8), 8×8 = 64 in the same way as -8 x -8 is also 64.
This is a trick they will often use on the GMAT, in particular with the Data Sufficiency questions as few people think of the negative possibility thus often making the statements insufficient.
- Every number has an exponent, even if it is not shown, numbers with exponents “¹” remain as they are and there is therefore no need to show the exponent. 5¹ is 5. Numbers to the power of 0 is always 1. So for example, 5⁰ is 1. This is true for any number to the power of “⁰”.
Subtractions and Additions of Exponents:
Those are the easy ones. For additions of exponents, for example 2² + 2³ = 2⁵. The important condition with subtractions of exponents is that the base has to be the same for both side you are adding up. If you have are subtraction
Division and multiplication of Exponents:
The important thing in dividing or multiplying exponents is to make sure that the base is always the same.
Multiplications is simply an addition. In the case of 2² x 2³ the result is 2²⁺³ which is 2⁵
Division is simply a substraction 2³/2² than you can just subtract the exponents from each other so you would then get 2³ – 2² = 2¹ which is equal to 2. It is important in this operation to remember that you need to subtract the top number (numerator) with the bottom number (denominator), not the other way round.
If you find yourself of having two sets of exponents for the same base such as: (2⁵)² then you simply take the two exponents and multiply them to get a single exponent, in this case it is 2¹⁰ .
Square Roots
Roots is the opposite of exponents. Usually demonstrated by this symbol: √. For example the Square Root of 25 is written: √25. This means that the square root of 25 (√25) is 5 as 5² is 25.
About: Exponents, GMAT, Quantitative, Square Root
