Squares and Cubes
Part of the Numbers & Operations section of Coddy's Pre-Algebra journey. Lesson 35 of 60.
Two exponents have names of their own. A number to the power 2 is squared: 5^2, read five squared, is 5 × 5, which is 25. The name comes from geometry. A square with sides 5 long holds 5 rows of 5 small unit squares, so its area is 5^2.
A number to the power 3 is cubed: 3^3, three cubed, is 3 × 3 × 3, which is 27. A cube with edges 3 long is built from 3 layers, each a 3 by 3 square of small cubes, so its volume is 3^3.
When powers sit in a sum, work out each power first and add after: 5^2 + 3^3 becomes 25 + 27, which is 52. Each power is one number in a compact package, so it has to be opened before it can be added.
Challenge
Work out 4^2 + 2^3. Work out both powers in your first line, then add.
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 Numbers & Operations
1Working on the Board
Your First AnswerType the Next LineOne Line at a TimeDots and BarsFriendly ProductsRecap: Board Work4Adding Integers
Adding Two NegativesDifferent SignsZero PairsAdding Several IntegersRecap: Adding Integers7Exponents
Repeated MultiplicationSquares and CubesPowers of TenNegative BasesWhere the Minus SitsRecap: Exponents2Order of Operations
Multiply Before AddingLeft to RightParentheses FirstBrackets Inside BracketsThe Fraction Bar GroupsRecap: Order of Operations5Subtracting Integers
Add the OppositeSubtracting a NegativePlus and Minus in a RowDistance Between NumbersRecap: Subtracting Integers