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Warm Up Evaluate.

Explore the fundamentals of exponents, including multiplying and dividing powers, zero power, negative exponents, and more. Improve your skills in algebra and number manipulation!

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Warm Up Evaluate.

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  1. 2-7 Properties of Exponents Course 3 Warm Up Evaluate. 27 1. 33 2. 4 • 4 • 4 • 4 256 3.b2 for b = 4 16 4. n2r for n = 3 and r = 2 18

  2. 2-7 Properties of Exponents Course 3 Learn to apply the properties of exponents and to evaluate the zero exponent.

  3. 2-7 Properties of Exponents Course 3 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

  4. 2-7 Properties of Exponents MULTIPLYING POWERS WITH THE SAME BASE Numbers Algebra Words To multiply powers with the same base, keep the base and add the exponents. bm • bn = bm+ n 35• 38 = 35 + 8 = 313 Course 3

  5. 2-7 Properties of Exponents A. 66 •63 6 6 + 3 6 9 n 5 + 7 n 12 Course 3 Additional Example 1A & 1B: Multiplying Powers with the Same Base Multiply. Write the product as one power. Add exponents. B. n5 •n7 Add exponents.

  6. 2-7 Properties of Exponents 1 Think: 2 = 2 2 5 + 1 2 6 24 4 + 4 24 8 Course 3 Additional Example 1: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. C. 25 • 2 Add exponents. D.244• 244 Add exponents.

  7. 2-7 Properties of Exponents A. 42 •44 4 2 + 4 4 6 x 2 + 3 x 5 Course 3 Try This: Example 1A & 1B Multiply. Write the product as one power. Add exponents. B. x2 •x3 Add exponents.

  8. 2-7 Properties of Exponents 5555 5 5555 5 5 5 = = = 5 •5 = 52 555 555 53 DIVIDING POWERS WITH THE SAME BASE Words Numbers Algebra To divide powers with the same base, keep the base and subtract the exponents. 6 b 9 m = = = 6 b 6 9 – 4 m – n 5 6 b 4 n Course 3 Notice what occurs when you divide powers with the same base.

  9. Remember Multiply: add exponents Divide: subtract exponents

  10. 2-7 Properties of Exponents 10 – 9 5 – 3 7 x 2 10 5 9 3 7 7 x 7 x Think: x = x 1 Course 3 Additional Example 2: Dividing Powers with the Same Base Divide. Write the product as one power. A. Subtract exponents. B. Subtract exponents. x

  11. 2-7 Properties of Exponents 9 – 2 9 10 – 5 e 5 e Course 3 Try This: Example 2 Divide. Write the product as one power. 9 9 A. 9 2 Subtract exponents. 97 e 10 B. e 5 Subtract exponents.

  12. 2-7 Properties of Exponents THE ZERO POWER Algebra Words Numbers The zero power of any number except 0 equals 1. 1000 = 1 a0= 1, if a 0 (–7)0 = 1 Course 3 Anything to the zero power equals 1

  13. 2-7 Properties of Exponents Course 3 Negative Exponents When you have a negative exponent, take the reciprocal and make the exponent positive.

  14. 2-7 Properties of Exponents n 7 8 9 109 4 10 105 t 2 t9 t7 Course 3 Lesson Quiz: Part 1 Write the product or quotient as one power 1. n3n4 2. 8 • 88 3. 4. 5.

  15. 2-7 Properties of Exponents Course 3 Lesson Quiz: Part 2 6. A school would like to purchase new globes. They can get six dozen for $705.80 from Company A. From Company B, they can buy a half gross for $725.10. Which company should they buy from? (1 gross = 122 items) Company A

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