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Multiplication Properties of Exponents

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- 1. Warm UpWrite each expression using an exponent.1. 2 • 2 • 2 232. x • x • x • x3.Write each expression without using anexponent.4. 43 4 • 4 • 45. y2 y • y6. m–4
- 2. You have seen that exponential expressions areuseful when writing very small or very largenumbers. To perform operations on these numbers,you can use properties of exponents. You can alsouse these properties to simplify your answer.In this lesson, you will learn some properties thatwill help you simplify exponential expressionscontaining multiplication.
- 3. Products of powers with the same base can befound by writing each power as a repeatedmultiplication.Notice the relationship between the exponents inthe factors and the exponents in the product5 + 2 = 7.
- 4. Example 1: Finding Products of PowersSimplify.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.
- 5. Example 1: Finding Products of PowersSimplify. C. Group powers with the same base together. Add the exponents of powers with the same base. D. Group the positive exponents and add since they have the same base Add the like bases. 1
- 6. Remember!A number or variable written without an exponentactually has an exponent of 1. 10 = 101 y = y1
- 7. Check It Out! Example 1Simplify.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.
- 8. Check It Out! Example 1Simplify. c. Group powers with the same base together. Add.
- 9. Check It Out! Example 1Simplify. d. Group the first two and second two terms. Divide the first group and add the second group. Multiply.
- 10. 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 mi group.
- 11. 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. Use the Commutative and Associative Properties to group. Multiply within each group.
- 12. To find a power of a power, you can use themeaning of exponents.Notice the relationship between the exponents inthe original power and the exponent in the finalpower:
- 13. Example 3: Finding Powers of PowersSimplify. Use the Power of a Power Property. Simplify. Use the Power of a Power Property. Zero multiplied by any number is zero 1 Any number raised to the zero power is 1.
- 14. Example 3: Finding Powers of PowersSimplify.C. 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.
- 15. Check It Out! Example 3Simplify. Use the Power of a Power Property. Simplify. Use the Power of a Power Property. Zero multiplied by any number is zero. 1 Any number raised to the zero power is 1.
- 16. Check It Out! Example 3cSimplify. c. Use the Power of a Power Property. Simplify the exponents of the two terms. Since the powers have the same base, add the exponents.
- 17. Powers of products can be found by using themeaning of an exponent.
- 18. Example 4: Finding Powers of ProductsSimplify. A. Use the Power of a Product Property. Simplify. B. Use the Power of a Product Property. Simplify.
- 19. Example 4: Finding Powers of ProductsSimplify.C. Use the Power of a Product Property. Use the Power of a Product Property. Simplify.
- 20. Check It Out! Example 4Simplify. Use the Power of a Product Property. Simplify. Use the Power of a Product Property. Use the Power of a Product Property. Simplify.
- 21. Check It Out! Example 4Simplify.c. Use the Power of a Product Property. Use the Power of a Product Property. Combine like terms. Write with a positive exponent.
- 22. Lesson Quiz: Part ISimplify.1. 32• 34 2.3. (x3)2 4.5. 6.7.
- 23. Lesson Quiz: Part II7. The islands of Samoa have an approximate area of 2.9 103 square kilometers. The area of Texas is about 2.3 102 times as great as that of the islands. What is the approximate area of Texas? Write your answer in scientific notation.

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