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An overview of the rules for working with exponents in algebra, including the zero rule, rules of 1, product rule, quotient rule, negative exponents, and power rule. Examples are given to illustrate each rule and common errors to avoid.
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Rules of Exponents Name
Example:
base: 5 exponent: 2 power: 2nd read: five squared or five to the second power
Exponents are used in many algebra problems, so it's important that you understand the rules for working with exponents. Let's go over each rule in detail, and see some examples.
Zero Rule According to the "zero rule," any nonzero number raised to the power of zero equals 1. Rules of 1 There are two simple "rules of 1" to remember. First, any number raised to the power of "one" equals itself. This makes sense, because the power shows how many times the base is multiplied by itself. If it's only multiplied one time, then it's logical that it equals itself. Secondly, one raised to any power is one. This, too, is logical, because one times one times one, as many times as you multiply it, is always equal to one.
Product Rule The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents. In this example, you can see how it works. Adding the exponents is just a short cut!