Section 1 4 Exponential Notation Order of Operations

Section 1. 4 Exponential Notation. Order of Operations.

Exponential Notation Like multiplication which was originally introduced as a shortcut for repetitive addition, exponential notation was originally introduced as a shortcut for repetitive multiplication: The number 2 that is multiplied is called a base, 12 the number of times the base is multiplied is called an exponent.

Definition Exponential Notation If number b is multiplied by itself n times, this product could be shortly written as This form is called exponential notation. The number b that is multiplied is called a base, n the number of times the base is multiplied is called an exponent.

Example: a. Rewrite in exponential notation b. Evaluate exponential expression by repetitive multiplication

Example: Evaluate an expression: 1. If we evaluate addition first and then multiplication, we will get 2. If we evaluate multiplication first and then addition, we will get In the example above the result depended on the order in which we execute different operations. When evaluating expressions with more than one operation we need to know which operation should be done first, which next. In other words we need to know the order of operations.

The Order of Operations 1. 2. 3. 4. 5. If there any grouping symbols, such as parenthesis ( ), square brackets [ ], curly braces { } or the other grouping symbols perform all the operations within the grouping symbols first. Evaluate all the exponential expressions. Do all negations; put all negative numbers in the parenthesis. Do all multiplications and divisions from left to right. Do all additions and subtractions from left to right.

Example: Evaluate an expression

Properties of Algebraic Operations 1. Addition of any number to 0 or 0 to any number always results in 0 an original number. 2. Multiplication of any number by 0 or 0 by any number always results in 0 3. Multiplication of any number by 1 or 1 by any number always results in an original number

Commutative Property Of Addition The sum of any two numbers a and b does not depend on the order in which they are added Of Multiplication The product of any two numbers a and b does not depend on the order in which they are multiplied

Associative Property Of Addition �The sum of any three numbers a, b and c does could be found by grouping the numbers in any order of addition Of Multiplication The product of any three numbers a, b and c does could be found by grouping the numbers in any order of multiplication

Distributive Property If an expression in parenthesis is multiplied by a factor, to open the parenthesis, multiply each term inside of the parenthesis by this factor