Squares and Cubes
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 2 of 64.
Two exponents are so common they have names. Raising to the second power is squaring: 5^2 is "five squared", and it is exactly the area of a square with side 5. Raising to the third power is cubing: 4^3 is "four cubed", the volume of a cube with edge 4.
The names carry the geometry, but the arithmetic is just factor counting: 5^2 = 5 * 5 = 25 and 4^3 = 4 * 4 * 4 = 64. Higher exponents drop the geometry and keep the pattern: 3^5 is "three to the fifth".
Powers grow fast. Doubling a number doubles it once; squaring 10 gives 100, cubing it gives 1000. That speed is why exponents get their own rules instead of being multiplied out every time.
Challenge
EasyUnpack 5^3, five cubed, and multiply it down line by line.
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