Using the Zero Exponent Rule of Exponents
Return to the quotient rule. We made the condition that so that the difference would never be zero or negative. What would happen if ? In this case, we would use the zero exponent rule of exponents to simplify the expression to 1. To see how this is done, let us begin with an example.If we were to simplify the original expression using the quotient rule, we would have
If we equate the two answers, the result is . This is true for any nonzero real number, or any variable representing a real number.
The sole exception is the expression . This appears later in more advanced courses, but for now, we will consider the value to be undefined.
A General Note: The Zero Exponent Rule of Exponents
For any nonzero real number , the zero exponent rule of exponents states thatExample 4: Using the Zero Exponent Rule
Simplify each expression using the zero exponent rule of exponents.Solution
Use the zero exponent and other rules to simplify each expression.- \begin{array}\text{ }\frac{c^{3}}{c^{3}} \hfill& =c^{3-3} \\ \hfill& =c^{0} \\ \hfill& =1\end{array}
Try It 4
Simplify each expression using the zero exponent rule of exponents.a. b. c. d.
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- College Algebra. Provided by: OpenStax Authored by: OpenStax College Algebra. Located at: https://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1/Preface. License: CC BY: Attribution.