Powers Before Products
Part of the Numbers & Operations section of Coddy's Pre-Algebra journey. Lesson 46 of 60.
You now have every piece of the order of operations. First anything that groups: parentheses, fraction bars, root signs and absolute value bars. Then powers and roots. Then multiplication and division. Last, addition and subtraction.
So in 2 × 3^2 the power goes first: 3^2 is 9, and 2 × 9 is 18. Multiplying first would give 6^2, which is 36, a different number. The exponent sits on the 3 alone, and a power is a product already packaged around its base, so it is finished before the base can be used.
Many people remember the order as PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. The word hides a trap. M comes before D in it, but multiplication does not go before division: they share a rank. So do addition and subtraction, and within a rank you work left to right.
Challenge
Work out 4 × 2^3 - 5, one step per 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 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 Integers2Order 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 Integers6Multiplying and Dividing
Negative Times PositiveTwo NegativesCounting the NegativesDividing IntegersZero in DivisionRecap: Multiply and Divide9Putting It All Together
Powers Before ProductsNegatives InsideNegative Bases in SumsEverything at OnceRecap: The Full Order