Exponents and Order of Operations

Exponents Exponents can be one of those math areas where we make mistakes. There are two parts to an exponent: the Base and the Exponent 5 2 means we multiply the base – which is 5 – by itself 2 times or 5 x 5 = means we multiply the base – which is 3 – by itself 4 times or 3 x 3 x 3 x 3 = 81 Note: Never multiply the base by the exponent. You’ll get a wrong answer every time!

Practicing Exponents (3) 2 (-4) 2 Try them and then click here to see if you got the right answer.click here

Answers to Practice Problems 4 4 = = = = = 243 -(3) 2 = -9 (-4) 2 = 16 -(3) 2 (-4)2 Word of caution regarding the last two examples. Remember that the exponent only belongs to what it is directly sitting next to. In -(3) 2 the 2 means you will only square what is inside the parenthesis, not the negative sign outside the parenthesis. In the example (-4)2 the two means you will square everything inside the parenthesis.

PEMDAS ParenthesesExponentsMultiplicationDivisionAdditionSubtraction Working left to right Order does not matter An easy way to remember the Order of Operations is ……

Otherwise Known As…. Please (parentheses) Excuse (exponents) My (multiplication) Dear (division) Aunt (addition) Sally (subtraction) Please Excuse My Dear Aunt Sally

Examples 6 / –Following the order of operations, we would first look for parentheses. Since there are none, we go to the exponents next. We have an exponent so we figure it out first. 5 2 is the same as 5 x 5 which equals 25. So the equation now looks like: 6 / –Next our order of operations tells us we need to do multiplication/division starting from the left and working to the right. So we do 6 / 3 which is equal to 2. Our equation now looks like: –Now doing the addition/subtraction next we simply add the to get 27.

Showing Your Work In the previous example, you would show your work as follows: 6 / / Notice that there are no equal signs in the problem. Start each step on a new line. Being neat and orderly will be a huge help!

Practicing Order of Operations – 6 2 2(8 – 3) 2 + (5 – 2) + 4 2

More Practice 12 5 – – |8 – 2| – |13 – 5|

And More… (5 + 3) [5 + 2(8 – 3)] |6 – 2| (8 – 5)