Final: Three Rules, One Line
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 59 of 64.
When an expression uses several exponent rules, work from the inside out. First simplify the power of a power by multiplying the exponents. Then multiply the powers with the same base by adding their exponents. Then divide by subtracting the exponents.
For (x^2)^3 × x ÷ x^4: the power of a power gives (x^2)^3 = x^6. The product gives x^6 × x = x^7, because x on its own has exponent 1. The quotient gives x^7 ÷ x^4 = x^3.
Challenge
MediumSimplify (x^4)^2 * x / x^3 to a single power of x.
Try it yourself
Simplify the expression
This 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 Negative9Adding and Subtracting
Adding PolynomialsSubtracting PolynomialsThe Minus Reaches EverythingPerimeter as a PolynomialRecap: Add and Subtract12Final Challenges
Final: Three Rules, One LineFinal: Scientific NotationFinal: The Big TidyFinal: Area, ModeledFinal: Area, ExpandedFinal: Divide and Conquer