Every Factor Gets the Power
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 21 of 64.
(ab)^2 means two copies of the whole product ab multiplied together: ab × ab. You can multiply factors in any order, so group the letters: a × a × b × b, which is a^2 b^2.
The power of a product rule says that an exponent on a product in parentheses applies to every factor inside: (ab)^n = a^n b^n. The example shows why. Each copy of ab brings one a and one b, so two copies give two of each.
The rule does not work over addition. (a + b)^2 is not a^2 + b^2. A later lesson in this section shows what (a + b)^2 really equals. Factors in a product share the power. Terms in a sum do not.
Challenge
EasyWrite (a^2 b)^3 without the outer power.
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