Dividing Same Bases
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 11 of 64.
Division undoes multiplication factor by factor. x^5 / x^2 is five factors of x over two factors of x, and each factor below cancels one factor above: two pairs cancel, three factors survive on top. x^5 / x^2 = x^3.
That is the quotient rule: same base, subtract the exponents, top minus bottom. It is the product rule run backwards, and it has the same fine print: the bases must match, or nothing cancels.
Subtraction keeps the order: 5 - 2, the exponent above minus the exponent below. Cancelling is the reason; the subtraction is just the count of what survives.
Challenge
EasyWrite x^9 / x^7 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