All Three Rules Together
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 24 of 64.
Real expressions mix the laws. (x^2)^3 * x^4 has a nested power standing beside a plain one. Work the shapes from the inside out: the nest first, (x^2)^3 = x^6, and then the side-by-side product, x^6 * x^4 = x^10.
Inside out is the reliable order: resolve each parenthesis to a single power, then let the product and quotient rules combine what remains. Each step is one law, named before it is used.
If two moves both seem legal, both are: the laws never disagree. x^6 * x^4 and (x^2)^5 describe the same ten factors.
Challenge
EasySimplify (x^3)^2 * x^5 to a single power.
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