With a Number Inside
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 22 of 64.
The factors inside a parenthesis do not have to be letters. (3y)^2 holds the factors 3 and y, and each takes the power: 3^2 * y^2. The number's power can then be evaluated on the spot: 9y^2.
This is the slip the lesson exists for: squaring 3y squares the 3 too. (3y)^2 is 9y^2, never 3y^2. Doubling a side of a square quadruples its area for exactly this reason.
The finished habit: power on a parenthesis, distribute it to every factor, then evaluate the numeric ones.
Challenge
EasyRewrite (4t)^2 with the power applied to each factor, numbers evaluated. Type the result.
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