Working with exponents is not as difficult as it seems, especially if you know the function of an exponent. Learning the function of exponents helps you understand the rules of exponents, making processes such as addition and subtraction much simpler. This article focuses on the exponent rules for addition, but once you learn these basic rules, most exponential functions will be less of a mystery.
While it may seem elementary to review addition, it is important to remember that math is not merely a set of numbers on a page or a puzzle to work out. Math---particularly addition---is a function. Addition is a function that helps account for a large quantity of items. Memorizing numerous addition equations as a child helps you to quickly work out much larger equations to account for impossibly large quantities. If you have not memorized your basic addition equations (perhaps you were absent that day or just never learned them), take the time to do that first. You should be able to add at least single digits instantaneously, without counting on your fingers. Otherwise, adding exponents will be a chore no matter how well you understand them.
Exponents are all about multiplication. An exponent tells you how many times to multiply a number by itself. For example, 5 to the 4th power (5^4 or 5 e4) tells you to multiply 5 by itself 4 times: 5 x 5 x 5 x 5. The number 5 is the base number and the number 4 is the exponent. Sometimes, however, you do not know the base number. In this case, a variable such as "a" will stand in place of the base number. So when you see "a" to the power of 4, it means that whatever "a" is will be multiplied by itself 4 times. Often when you do not know the exponent, the variable "n" is used, as in "5 to the power of n."
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Rule 1: Addition and the Order of Operations
The first rule to remember when adding with exponents is the order of operations: parenthesis, exponents, multiplication, division, addition, subtraction. This order of operations places exponents second in the solving scheme. So if you know both the base and the exponent, solve them before moving on. Example: 5^3 + 6^2 Step 1: 5 x 5 x 5 = 125 Step 2: 6 x 6 = 36 Step 3 (solve): 125 + 36 = 161
Rule 2: Multiplying the Same Base With Different Exponents
Multiplying exponents is easy when the bases are the same. The rule for multiplying exponents says that you can add the exponent of the first base to the exponent of the second base to simplify your problem. Example:
a^2 x a^3 = a^2+3 = a^5
What Not to Do
Rule 1 assumes that you know both the bases and the exponents. You cannot solve the exponent portion of the equation without all the information. Don't try to force a solution. a^4 + 5^n cannot be simplified without more information. Rule 2 applies only to bases that are the same. For example, a^2 x b^3 does not equal ab^5. Both exponents must have the same base before they can be added. Rule 2 applies to the multiplication of bases only. If you multiply y to the power of 4 (y^4) by y to the power of 3 (y^3), you may add the exponents 3+4. If you want to multiply y to the power of 4 (y^4) by z to the power of 3 (z^3), you will need more information. In the latter case, do not add the 4+3 exponents.