A Power Raised Again
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 16 of 64.
(x^3)^2 raises a power to a power: the base of the outer exponent is the whole package x^3. The outer 2 says "two copies of the package": x^3 * x^3. Each package holds three factors of x, so two packages hold six: (x^3)^2 = x^6.
That is the power of a power rule: the exponents multiply. Three factors per package, times two packages: 3 * 2 = 6 factors in all. It is counting again, one level up.
The parentheses are what make it this rule: they hand the whole power to the outer exponent, the same way they handed a whole negative number to an exponent in chapter one.
Challenge
EasyWrite (x^7)^2 as a single power of x.
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