With Coefficients
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 7 of 64.
5x^2 * 3x^4 mixes two kinds of factors: plain numbers and powers of x. Multiplication does not care about the order of factors, so gather each kind: the numbers 5 and 3 multiply to 15, and x^2 * x^4 combines by the product rule to x^6. Together: 15x^6.
The habit to build: numbers multiply, exponents add. The two operations live side by side in the same expression and never interfere: the coefficient counts how many, the exponent counts factors of x.
Watch for the classic slip of adding the coefficients: 5 * 3 is 15, not 8. The exponents are the ones that add.
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