Properties of Exponents I Exponential Notation Negative Exponents

Vocabulary Monomial-”One Term” consisting of numbers and variables. Monomials: x 2, 5, 3xy, 5x 5 y 2 Not Monomials: x+y, 2x 2 – 3x + 2, 4x 2 – 3x 2 y Base-The expression being raised to a power. Exponent-Identifies how many times a base is multiplied by itself.

Exponents Look at the following examples and identify the base: 5 3 x 2 (-2x) 2 (3xy 2 ) 5 Remember! The base is the number (or product) that is being raised to the power.

Exponential Notation There are reasons in mathematics that we may end up multiplying a number by itself many, many times. Instead of possibly multiplying a number by itself, say 15 times (only an example), we have the existence of exponential notation. This is meant to reduce the amount of numbers (or variables) we need to write out. It is a form shorthand.

Exponential Notation 5 x 5 x 5 x 5 x 5 x 5 x 5 = 78,125 Instead of writing all of that out, we can dramatically reduce that and write it as 5 7 = 78,125. In algebra though, we often work with variables. The exponent in exponential notation represents the number times that number or variable (referred to as the BASE ) is multiplied by itself.

Exponential Notation a x a x a ….x a = a n Here, we multiplied a by itself n times.

Exponential Notation Let’s look at some examples (given in class)

Negative Exponents One of our goals when we simplify an expression is to write that expression using all positive exponents. Negative exponents move the BASE from one part of the fraction to the other. When this occurs, the exponent becomes positive. Before you move anything, simplify the base as much as possible, then correctly identify what the base is.

Negative Exponents Once you see a negative exponent, simplify the base, then move it to the opposite part of the fraction, then continue simplifying. Let’s look at some examples (given in class)