Negative Bases
Part of the Numbers & Operations section of Coddy's Pre-Algebra journey. Lesson 37 of 60.
A negative number can be a base too, written in parentheses: (-5)^2 means (-5) × (-5). Two negatives multiply to a positive, so (-5)^2 is 25.
Add one more factor: (-5)^3 is (-5) × (-5) × (-5). Multiply one pair at a time. The first pair gives 25, so the next line is 25 × (-5), which is -125. The third negative factor had no partner, so it turned the result negative again.
That gives a rule you can read straight off the exponent. Negative factors pair up, and each pair makes a positive. With an even exponent every factor has a partner, so the result is positive. With an odd exponent one negative is left over, so the result is negative.
Challenge
Work out (-3)^3. Tap the power and choose the move that writes it as repeated multiplication, then multiply 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 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