Squares and Cubes
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 2 of 64.
Two exponents are so common that they have their own names. Raising a number to the second power is squaring. 5^2 is read "five squared", and it equals the area of a square with side 5. Raising a number to the third power is cubing. 4^3 is read "four cubed", and it equals the volume of a cube with edge 4.
The names come from geometry, but the arithmetic is still counting factors: 5^2 = 5 × 5 = 25 and 4^3 = 4 × 4 × 4 = 64. Higher powers have no special name. 3^5 is read "three to the fifth".
Powers grow fast. Doubling 10 gives 20, but squaring 10 gives 100 and cubing 10 gives 1000. Because powers grow so fast, exponents have rules of their own. You will learn them in this section, so that you do not have to multiply the factors out every time.
Challenge
EasyWrite 5^3, five cubed, as repeated multiplication, then multiply the factors one pair at a time.
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