More Than Two Factors
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 8 of 64.
The product rule chains: x^2 * x^5 * x is two factors, then five more, then one more. All of them are factors of the same x, so the counts add straight across: 2 + 5 + 1 = 8, and the product is x^8.
The last factor hides its exponent. A bare x is x^1: one factor of x. The 1 is never written, exactly as the coefficient 1 is never written, but it counts. Forgetting it is the one slip this lesson exists to prevent.
However many powers of one base are multiplied, the answer is one power whose exponent is the total count. The rule is not "two at a time"; it is bookkeeping for all the factors at once.
Challenge
EasyWrite x^6 * x^2 * x as a single power. Mind the bare x.
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