With Coefficients
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 13 of 64.
When a quotient has coefficients, you divide the coefficients and subtract the exponents. In 12x^5 / (4x^2), divide the numbers first: 12 / 4 = 3. Then apply the quotient rule to the powers: x^5 / x^2 = x^3. Put the two parts together to get 3x^3.
This works the same way as multiplying terms. When you multiply, the coefficients multiply and the exponents add. When you divide, the coefficients divide and the exponents subtract. The coefficient is an ordinary factor, and the exponent is a count of factors, so the two never mix.
If the coefficients do not divide evenly, write their quotient as a fraction. For nonzero x, 7x^5 / (2x^2) = (7/2)x^3. The powers still follow the quotient rule.
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