2. 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 9 2. Exponent Base Exponents

3. Exponential Form ReadMultiplyValue 10 1 Ten to the first power---10 10 2 Ten to the second power or ten squared 10 x 10100 10 3 10 4 Exponents

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

5. Finding the Value of Numbers Written in Exponential Form Example 1 8 3 = 8 x 8 x 8 = 512 Example 2 Try these: Find the value of the following numbers written in exponential form. 1.) 9 4 =2.) 1 5 = 3.) 4.1 2 =4.) Exponents

6. Comparing Exponents Example 1 10 1 __ 2 2 10 __ 2 x 2 10 _>_ 4 Try these: Compare the following numbers written in exponential form. Then, place a or = sign between them. 1.) 8 2 __ 4 3 2.) 25 1 __ 5 3 Evaluate the exponents Place the correct sign between the two numbers Example 2 4 3 __ 5 3 4 x 4 x 4 __ 5 x 5 x 5 64 _<_ 125 Evaluate the exponents Place the correct sign between the two numbers Exponents

7. Real-Life Application The zoo has an aquarium that holds 7 4 cubic gallons of water. How many gallons of water does the aquarium hold? Exponents