More Than Two Factors
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 8 of 64.
The product rule works for any number of powers. x^2 × x^5 × x is two factors of x, then five more, then one more. All of them are factors of the same base, so the counts add: 2 + 5 + 1 = 8. The product is x^8.
The factor x on its own means x^1. The exponent 1 is usually not written, but you must include it when you add the exponents.
However many powers of one base you multiply, the answer is one power. Its exponent is the total count of factors. You do not need to combine the powers two at a time. Add all the exponents at once.
Challenge
EasyWrite x^6 × x^2 × x as a single power. Remember that the bare x has the exponent 1.
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