With Coefficients
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 13 of 64.
12x^5 / (4x^2) carries numbers along with the powers, and each kind handles itself: the numbers divide, 12 / 4 = 3, and the powers follow the quotient rule, x^5 / x^2 = x^3. Together: 3x^3.
This mirrors the product chapter exactly. There, numbers multiplied while exponents added; here, numbers divide while exponents subtract. In both, the coefficient and the exponent never mix: one is an ordinary factor, the other is a count.
If the numbers do not divide evenly, they simply stay as a fraction: 7x^5 / (2x^2) is (7/2)x^3, and nothing else changes.
Challenge
EasySimplify 8x^6 / (2x^2) into a single term.
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