Multiplying Same Bases
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 6 of 64.
What is x^3 * x^4? Unpack both powers and count: x^3 is three factors of x, x^4 is four more, and multiplication just lines them all up: seven factors of x in a row. So x^3 * x^4 = x^7.
That is the product rule: when two powers of the same base are multiplied, the exponents add. Nothing mysterious happens; the exponents are counting factors, and putting two groups of factors together adds the counts.
The rule needs the bases to match. x^3 * y^4 has nothing to combine: three x's and four y's stay what they are. Same base, add the exponents; different bases, leave them alone.
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