MATH REVIEW: USEFUL MATH FOR EVERYONESECTION 3.2. WHAT IS AN EXPONENT? First let's look at how to work with variables to a given power, such as a^{3}. There are five rules for working with exponents:
Let's look at each of these in detail. 1. a^{m} * a^{n} = a^{(m+n)} says that when you take a number, a, multiplied by itself m times, and multiply that by the same number a multiplied by itself n times, it's the same as taking that number a and raising it to a power equal to the sum of m + n.
2. (a * b)^{n} = a^{n} * b^{n} says that when you multiply two numbers, and then multiply that product by itself n times, it's the same as multiplying the first number by itself n times and multiplying that by the second number multiplied by itself n times.
3. (a^{m})^{n} = a^{(m * n)} says that when you take a number, a , and multiply it by itself m times, then multiply that product by itself n times, it's the same as multiplying the number a by itself m * n times.
4. a^{m} / a^{n} = a^{(m-n)} says that when you take a number, a, and multiply it by itself m times, then divide that product by a multiplied by itself n times, it's the same as a multiplied by itself m-n times.
5. (a/b)^{n} = a^{n} / b^{n} says that when you divide a number, a by another number, b, and then multiply that quotient by itself n times, it is the same as multiplying the number by itself n times and then dividing that product by the number b multiplied by itself n times.
Understanding exponents will prepare you to use logarithms. For more information about this site contact the Distance Education Coordinator. Copyright © 2004 by the Regents of the University of Minnesota, an equal opportunity employer and educator. |