Every Factor Gets the Power
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 21 of 64.
What does (ab)^2 mean? Two copies of the whole product: ab * ab. Multiplication reorders freely, so gather the letters: a * a * b * b, which is a^2 b^2.
The power of a product rule: an exponent on a parenthesized product lands on every factor inside. (ab)^n = a^n b^n. The exponent distributes over multiplication.
It does not distribute over addition. (a + b)^2 is not a^2 + b^2, a fact with its own lesson later in this section. Factors share the power; terms do not.
Challenge
EasyWrite (a^2 b)^3 without the outer power. Type it onto the canvas.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
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