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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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Lesson 8.2 Apply Exponent Properties Involving Quotients After today’s lesson, you should be able to use properties of exponents involving quotients to.

Lesson 8.2 Apply Exponent Properties Involving Quotients After today’s lesson, you should be able to use properties of exponents involving quotients to.

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