1. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents 7-3 Multiplication Properties of Exponents Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Algebra 1

2. 7-3 Multiplication Properties of Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4. 4 3 5. y 2 6. m –4 2323 4 4 4 y

3. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Use multiplication properties of exponents to evaluate and simplify expressions. Objective

4. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents You have seen that exponential expressions are useful when writing very small or very large numbers. To perform operations on these numbers, you can use properties of exponents. You can also use these properties to simplify your answer. In this lesson, you will learn some properties that will help you simplify exponential expressions containing multiplication.

5. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents

6. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Products of powers with the same base can be found by writing each power as a repeated multiplication. Notice the relationship between the exponents in the factors and the exponents in the product 5 + 2 = 7.

7. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents

8. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Simplify. Example 1: Finding Products of Powers A. Since the powers have the same base, keep the base and add the exponents. B. Group powers with the same base together. Add the exponents of powers with the same base.

9. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Simplify. Example 1: Finding Products of Powers C. D. 1 Group powers with the same base together. Add the exponents of powers with the same base. Group the positive exponents and add since they have the same base Add the like bases.

10. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents A number or variable written without an exponent actually has an exponent of 1. Remember! 10 = 10 1 y = y 1

11. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Check It Out! Example 1 a. Simplify. Since the powers have the same base, keep the base and add the exponents. b. Group powers with the same base together. Add the exponents of powers with the same base.

12. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Check It Out! Example 1 Continued Simplify. c. Group powers with the same base together. Add the exponents of powers with the same base.

13. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Check It Out! Example 1 Continued Simplify. d. Use the definition x −n = and group the terms. Simplify. Add the exponents of powers with the same base. Multiply.

14. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Example 2: Astronomy Application Light from the Sun travels at about miles per second. It takes about 15,000 seconds for the light to reach Neptune. Find the approximate distance from the Sun to Neptune. Write your answer in scientific notation. distance = rate  time Write 15,000 in scientific notation. Use the Commutative and Associative Properties to group. Multiply within each group. mi

15. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Check It Out! Example 2 Light travels at about miles per second. Find the approximate distance that light travels in one hour. Write your answer in scientific notation. distance = rate  time Write 3,600 in scientific notation. Multiply within each group. Use the Commutative and Associative Properties to group.

16. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents To find a power of a power, you can use the meaning of exponents. Notice the relationship between the exponents in the original power and the exponent in the final power:

17. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents

18. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Simplify. Example 3: Finding Powers of Powers Use the Power of a Power Property. Simplify. 1 Use the Power of a Power Property. Zero multiplied by any number is zero Any number raised to the zero power is 1.

19. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Simplify. Example 3: Finding Powers of Powers Continued Use the Power of a Power Property. Simplify the exponent of the first term. Since the powers have the same base, add the exponents. Write with a positive exponent. C.

20. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Check It Out! Example 3 Simplify. Use the Power of a Power Property. Simplify. 1 Use the Power of a Power Property. Zero multiplied by any number is zero. Any number raised to the zero power is 1.

21. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Check It Out! Example 3c Continued Simplify. Use the Power of a Power Property. Simplify the exponents of the two terms. Since the powers have the same base, add the exponents. c.

22. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Powers of products can be found by using the meaning of an exponent.

23. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Example 4: Finding Powers of Products Simplify. Use the Power of a Product Property. Simplify. Use the Power of a Product Property. Simplify. A. B.

24. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Example 4: Finding Powers of Products Simplify. Use the Power of a Product Property. Use the Power of a Power Property. Simplify. C.

25. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Check It Out! Example 4 Simplify. Use the Power of a Product Property. Simplify. Use the Power of a Power Property. Use the Power of a Product Property. Simplify.

26. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Check It Out! Example 4 Continued Simplify. Use the Power of a Product Property. Use the Power of a Power Property. Combine like terms. Write with a positive exponent. c.

27. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Lesson Quiz: Part I Simplify. 1. 3 2 3 4 3. 5. 7. 2. 4. 6. (x3)2(x3)2

28. Holt McDougal Algebra 1 7-3 Multiplication Properties of Exponents Lesson Quiz: Part II 7. The islands of Samoa have an approximate area of 2.9  10 3 square kilometers. The area of Texas is about 2.3  10 2 times as great as that of the islands. What is the approximate area of Texas? Write your answer in scientific notation.