“Powers and Exponents” Monday, September 20 th

Do Now: Part 1 Simplify  2   3  3   5   4   6  6  6  ,776 Write the date, and each problem from the “Do Now” in your math notebooks.

Do Now: Part 2 Copy the following study team guidelines into your Math notebooks Study Team Guidelines 1.Each member of the study team is responsible for his or her own behavior. 2.Each member of the study team must be willing to help any other team member who asks for help. 3.When you have a question, ask your team or partner first. If no member of your team can answer, then ask the teacher for help. 4.All partner and team talk must remain focused on the learning we are doing. Save non academic talk for outside the classroom! 5.Use your team voice.

Learning Target: I can name the parts of a power expression and evaluate exponents.

Powers and Exponents A simple way to think of exponents and powers is as repeated multiplication m m m = m 3

Key Terms ofactor: when two or more numbers are multiplied together, each number is called a factor oexponent: an exponent tells how many times a number (called a base) is used as a factor opower: a number that is expressed using a base and an exponent base exponent

Powers and Exponents

Find each value. Evaluating Powers A = 4  4  4  4 = 256 B = 7  7  7 = 343 Use 4 as a factor 4 times. Use 7 as a factor 3 times. C = 19Use 19 as a factor 1 time.

Evaluating exponents Use 4 as a factor 3 times 4  4  4 = 16 Use 7 as a factor 2 times 7  7 = 49 Use 2 as a factor 7 times 2  2  2  2  2  2  2 = 128 Use 3 as a factor 5 times 3  3  3  3  3 = 243 Use 10 as a factor 6 times 10  10  10  10  10  10 = 1,000,000 Use 17 as a factor 1 time 17 1 = 17

To express a whole number as a power, write the number as the product of equal factors. Then write the product using the base and an exponent. For example, 10,000 = 10  10  10  10 = Exponents

Write each number using an exponent and the given base. Expressing Whole Numbers as Powers A. 625, base = 5  5  5  5 = is used as a factor 4 times. B. 64, base 2 64 = 2  2  2  2  2  2 = is used as a factor 6 times.

Write each number using an exponent and the given base 343, base 7 7  7  7 = , base 2 2  2  2  2  2  2  2  2 = 2 8 1,000,000,000 base  10  10  10  10  10  10  10  10 = 10 9

On Monday, Erik tells 3 people a secret. The next day each of them tells 3 more people. If this pattern continues, how many people besides Erik will know the secret on Friday? Application On Monday, 3 people know the secret. On Tuesday, 3 times as many people know as those who knew on Monday. On Wednesday, 3 times as many people know as those who knew on Tuesday. On Thursday, 3 times as many people know as those who knew on Wednesday.

On Friday, 3 times as many people know as those who knew on Thursday. Each day the number of people is 3 times greater. 3  3  3  3  3 = = On Friday 243 people besides Erik will know the secret Application: Continued

Scientists and mathematicians use exponential notation To describe very large and very small numbers. The average distance between the earth and the sun is 1 AU (astronomical unit) or about 93 million miles. We can write that number as Ninety three million 93,000, x 10 6 What advantage is there in using exponential notation to write very large numbers?

Today I learned … Today I learned … Quick Write:

Tonight’s Homework (due: Tuesday, 9/21) In your text book: Read: pg Read: pg Do: pg ; #16-22, and 48 Do: pg ; #16-22, and 48