A Power of a Quotient
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 23 of 64.
The same reordering works over a fraction bar. (x/y)^3 is three copies of the fraction, x/y * x/y * x/y, and fractions multiply top with top, bottom with bottom: x^3 / y^3.
The power of a quotient rule: the exponent lands on the numerator and the denominator alike. (a/b)^n = a^n / b^n, for any nonzero b.
Products, quotients, and nested powers now all pass exponents inward. The one structure that blocks an exponent at the door is a sum, and the multiplying chapter will show what actually happens there.
Challenge
EasyWrite (2x/y)^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