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**4-3 Properties of Exponents Warm Up Problem of the Day**

Course 3 Warm Up Problem of the Day Lesson Presentation

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Warm Up Evaluate. 1. 33 27 2. 4 • 4 • 4 • 4 256 3. b2 for b = 4 16 4. n2r for n = 3 and r = 2 18

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Problem of the Day Calculate 6 to the fourth power minus 56. 1240

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**Learn to apply the properties of exponents.**

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**The factors of a power, such as 74, can be grouped in different ways**

The factors of a power, such as 74, can be grouped in different ways. Notice the relationship of the exponents in each product. 7 • 7 • 7 • 7 = 74 (7 • 7 • 7) • 7 = 73 • 71 = 74 (7 • 7) • (7 • 7) = 72 • 72 = 74

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**Example 1: Multiplying Powers with the Same Base**

Multiply. Write the product as one power. A. 66 • 63 6 6 + 3 Add exponents. 6 9 B. n5 • n7 n 5 + 7 Add exponents. n 12

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**Example 1: Multiplying Powers with the Same Base Continued**

Multiply. Write the product as one power. C. 25 • 2 2 5 + 1 Think: 2 = 2 1 2 6 Add exponents. D. 244 • 244 24 4 + 4 Add exponents. 24 8

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**A. 42 • 44 4 Add exponents. 4 B. x2 • x3 x Add exponents. x**

Check It Out: Example 1 Multiply. Write the product as one power. A. 42 • 44 4 2 + 4 Add exponents. 4 6 B. x2 • x3 x 2 + 3 Add exponents. x 5

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**Cannot combine; the bases are not the same.**

Check It Out: Example 1 Multiply. Write the product as one power. C. x5 • y2 Cannot combine; the bases are not the same. x5 • y2 D. 412 • 417 41 2 + 7 Add exponents. 41 9

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**Notice what occurs when you divide powers with the same base.**

5 53 = 5 5 5 5 5 5 5 5 = 5 • 5 = 52

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**Example 2: Dividing Powers with the Same Base**

Divide. Write the quotient as one power. 7 5 3 A. 7 5 – 3 Subtract exponents. 7 2 x 10 9 B. x 10 – 9 Subtract exponents. x Think: x = x 1

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**A. B. 9 9 9 Subtract exponents. 97 e e e Subtract exponents. e**

Check It Out: Example 2 Divide. Write the product as one power. 9 9 A. 9 2 9 9 – 2 Subtract exponents. 97 e 10 B. e 5 e 10 – 5 Subtract exponents. e 5

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**RAISING A POWER TO A POWER**

Reading Math (9 ) is read as “nine to the fourth, to the fifth.” 5 4

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**Example 3: Raising a Power to a Power**

Simplify. A. (54)2 = 54 • 2 Multiply exponents. = 58 B. (67)9 Multiply exponents. = 67 • 9 = 663

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**Example 3: Raising a Power to a Power**

Simplify. C. (172) –20 Multiply exponents. = 172 • –20 = 17–40

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**A. (33)4 Multiply exponents. = 33 • 4 = 312 B. (48)2**

Check It Out: Example 3 Simplify. A. (33)4 Multiply exponents. = 33 • 4 = 312 B. (48)2 Multiply exponents. = 48 • 2 = 416

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**D. (134) –10 Multiply exponents. Check It Out: Example 3 Simplify.**

= 134 • –10 = 13–40

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Lesson Quiz Write the product or quotient as one power. 1. n3 n4 n 7 2. 8 • 88 8 9 t9 t7 109 105 3. 4. 10 4 t 2 5. 32 • 33 • 35 3 10 6. (m2)19 m38 7. (9-8)9 8. (104)0 1 9–72

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