Multiplying Same Bases
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 6 of 64.
What is x^3 × x^4? Write out both powers and count the factors. x^3 is three factors of x, and x^4 is four more. Multiplying them puts all seven factors in a row, so x^3 × x^4 = x^7.
The product rule says that when you multiply two powers of the same base, you add the exponents. The exponents count factors, and putting two groups of factors together adds the counts.
The product rule only works when the bases match. x^3 × y^4 has nothing to combine. Three factors of x and four factors of y stay as they are. When the bases are the same, add the exponents. When the bases are different, leave the powers as they are.
Challenge
EasyWrite x^5 × x^3 as a single power.
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