With Coefficients
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 7 of 64.
To simplify 5x^2 × 3x^4, group the numbers together and the powers of x together. The coefficients multiply: 5 × 3 = 15. The powers follow the product rule: x^2 × x^4 = x^6. The result is 15x^6.
When you multiply monomials, multiply the coefficients. Then, for each base that appears in both, add the exponents. These are two separate steps on different factors.
Do not add the coefficients. 5 × 3 is 15, not 8. Add the exponents only for the powers that have the same base.
Challenge
EasySimplify 6x^3 × 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