A Power Raised Again
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 16 of 64.
When a power is raised to another power, you multiply the exponents. The rule is called the power of a power rule.
In (x^3)^2, the base of the outer power is x^3. Squaring x^3 means multiplying it by itself: x^3 * x^3. Each copy of x^3 holds three factors of x, so there are six factors of x in total, and (x^3)^2 = x^6.
The example shows why the exponents multiply. There are three factors of x in each copy, and there are two copies, so there are 3 * 2 = 6 factors in all.
The parentheses make the whole inner power x^3 the base of the outer power. Both exponents count factors of x, so both are used when you simplify.
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