Exponents

Exponents Definitions: Exponent – Is the number that tells us how many times to multiply a number (called the base) by itself. Base – Is a number that is multiplied by itself when it is raised to an exponent. Exponential Form – Is the form of a number when it is written with a base and an exponent. Perfect Squares – Are numbers that are the squares of whole numbers. For example, 81 is a perfect square because it is the value of 92. Exponent Base

Exponents Exponential Form Read Multiply Value 101 Ten to the first power --- 10 102 Ten to the second power or ten squared 10 • 10 100 103 104

Writing Numbers in Exponential Form Exponents Writing Numbers in Exponential Form Example 1 7 • 7 • 7 = 73 Example 2 5 • 5 • 5 • 5 = 54 Try these: Write the following expressions in exponential form. 1.) 6 • 6 = 2.) 10 • 10 • 10 • 10 = 3.) 2 • 2 • 2 • 2 • 2 = 4.) 12 • 12 • 12 =

Finding the Value of Numbers Written in Exponential Form Exponents Finding the Value of Numbers Written in Exponential Form Example 1 83 = 8 • 8 • 8 = 512 Example 2 Try these: Find the value of the following numbers written in exponential form. 1.) 94 = 2.) 15 = 3.) 4.12 = 4.)

Exponents Comparing Exponents Example 1 Example 2 101 __ 22 10 __ 2 • 2 10 _>_ 4 Example 2 43 __ 53 4 • 4 • 4 __ 5 • 5 • 5 64 _<_ 125 Evaluate the exponents Evaluate the exponents Place the correct sign between the two numbers Place the correct sign between the two numbers Try these: Compare the following numbers written in exponential form. Then, place a <, > or = sign between them. 1.) 82 __ 43 2.) 251 __ 53

Real-Life Application Exponents Real-Life Application The zoo has an aquarium that holds 74 cubic gallons of water. How many gallons of water does the aquarium hold?