Where the Minus Sits
Part of the Numbers & Operations section of Coddy's Pre-Algebra journey. Lesson 38 of 60.
Compare (-4)^2 with -4^2. In (-4)^2 the parentheses make -4 the base, so it is (-4) × (-4), which is 16. In -4^2 there are no parentheses, and the power touches only the 4. It means the opposite of 4^2, so -4^2 is -16.
Why? A power belongs to whatever sits right under its exponent, and it is worked out before anything else in the line, including the minus sign in front. Think of -4^2 as 0 - 4^2: the power goes first, giving 0 - 16, and only then is the 16 taken away.
So when you meet a power, look at what is directly under the exponent. A closing parenthesis means the whole bracket is the base, sign included. A digit means only that number is, and any minus in front waits until the power is done.
Challenge
Work out -5^2 + (-1)^4. Look carefully at which power has its minus inside parentheses.
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