§ 1.8 Exponents and Order of Operations

Definition of Natural Number Exponent If b is a real number and n is a natural number, b is the base and n is the exponent. is read “the nth power of b” or “b to the nth power”. Blitzer, Introductory Algebra, 5e – Slide #2 Section 1.8

Simplifying algebraic expressions that contain exponents. Blitzer, Introductory Algebra, 5e – Slide #3 Section 1.8

Simplifying algebraic expressions that contain exponents. Blitzer, Introductory Algebra, 5e – Slide #4 Section 1.8 In this example, you can see that we combined under addition only “like terms”. The variable parts of terms must be the same for them to be “like terms”. Note that we stopped after we had combined like terms. We can not go farther in simplifying in this example.

Order of Operations 1.Perform all operations within grouping symbols. (Starting with innermost.) 2.Evaluate all exponential expressions. 3.Do all multiplications and divisions in the order they occur, working left to right. 4.Finally, do all additions and subtractions in the order in which they occur, working left to right. Blitzer, Introductory Algebra, 5e – Slide #5 Section 1.8

Examples: Order of Operation Blitzer, Introductory Algebra, 5e – Slide #6 Section 1.8

Example: Order of Operations Blitzer, Introductory Algebra, 5e – Slide #7 Section 1.8

Example: Using Order of Operations Blitzer, Introductory Algebra, 5e – Slide #8 Section 1.8

In evaluating expressions, what comes first? #1 Start with the parentheses. Parentheses say “Me First!” #2 Then evaluate the exponential expressions. #3 Multiplications and divisions are equal in the order of operations – Perform them next. #4 Additions and subtractions are also equal to each other in order – and they come last. Remember by “PEMDAS” - parentheses, exponents, multiplication, division, addition, subtraction Blitzer, Introductory Algebra, 5e – Slide #9 Section 1.8

Blitzer, Introductory Algebra, 5e – Slide #10 Section 1.8 Order of Operations - PEMDAS Order of Operations 1) First, perform all operations within grouping symbols 2) Next, Evaluate all exponential expressions. 3) Next, do all multiplications and divisions in the order in which they occur working from left to right. 4) Finally, do all additions and subtractions in the order in which they occur, working from left to right.

Blitzer, Introductory Algebra, 5e – Slide #11 Section 1.8 Order of Operations - PEMDAS Evaluate for. EXAMPLE Replace R with 3 Evaluate inside parentheses first Evaluate – first exponent SOLUTION

Blitzer, Introductory Algebra, 5e – Slide #12 Section 1.8 Order of Operations - PEMDAS -135Subtract Multiply CONTINUED (81) Evaluate – second exponent

Blitzer, Introductory Algebra, 5e – Slide #13 Section 1.8 Order of OperationsEXAMPLE Simplify. SOLUTION Evaluating exponent Multiply Divide Subtract