The Zero Exponent
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 26 of 64.
The quotient rule leads to a new kind of exponent. x^7 / x^7 is a nonzero number divided by itself, so its value is 1. The quotient rule says to subtract the exponents: 7 - 7 = 0, which gives x^0.
Both answers describe the same expression, so they must be equal. For nonzero x, x^0 = 1. The example shows that the zero exponent follows from the quotient rule.
You can also think about the factors. x^3 means three factors of x, and x^0 means no factors of x at all. A product with no factors is 1, just as a sum with no terms is 0.
Challenge
EasySimplify x^3 * x^2 / x^5.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Exponents & Polynomials
1What a Power Is
Repeated MultiplicationSquares and CubesPowers of Negative NumbersWhere the Minus LivesRecap: First Powers4Power of a Power
A Power Raised AgainWhy Exponents MultiplyProduct Rule or Power Rule?The Rule in LettersRecap: Power of a Power2The Product Rule
Multiplying Same BasesWith CoefficientsMore Than Two FactorsThe Rule in LettersRecap: The Product Rule5Product and Quotient Powers
Every Factor Gets the PowerWith a Number InsideA Power of a QuotientAll Three Rules TogetherRecap: Products and Quotients8What a Polynomial Is
Terms with PowersThe DegreeLike Terms, Only StrongerRecap: Meet the Polynomials11Dividing by a Monomial
Splitting the FractionDividing by a Variable TermBigger SplitsCancel with CareRecap: Dividing3The Quotient Rule
Dividing Same BasesWhy Exponents SubtractWith CoefficientsThe Rule in LettersRecap: The Quotient Rule6Zero and Negative Exponents
The Zero ExponentZero at WorkNegative Means ReciprocalWriting Without NegativesPowers of TenRecap: Zero and Negative