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

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

3. The factors of a power, such as 7 4, can be grouped in different ways. Notice the relationship of the exponents in each product. Course 3 2-7 Properties of Exponents 7 7 7 7 = 7 4 (7 7 7) 7 = 7 3 7 1 = 7 4 (7 7) (7 7) = 7 2 7 2 = 7 4

4. Course 3 2-7 Properties of Exponents Words NumbersAlgebra To multiply powers with the same base, keep the base and add the exponents. b m b n = b m + n 3 5 3 8 = 3 5 + 8 = 3 13 MULTIPLYING POWERS WITH THE SAME BASE

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

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

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

8. Course 3 2-7 Properties of Exponents Notice what occurs when you divide powers with the same base. DIVIDING POWERS WITH THE SAME BASE WordsNumbersAlgebra To divide powers with the same base, keep the base and subtract the exponents. 6 5 6 9 – 4 6 9 6 4 = = b m – n b m b n = 5 5 5353 = 5  5  55  5  5 5  5  5  5  5 = 5 5 = 5 2 = 5  5  55  5  5 5  5  5  5  5

9. Remember Multiply: add exponents Divide: subtract exponents

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

11. Course 3 2-7 Properties of Exponents Subtract exponents. 9797 9 9 – 2 9 9 9 2 Try This: Example 2 Divide. Write the product as one power. A. B. e 10 e 5 Subtract exponents. e 10 – 5 e 5

12. Course 3 2-7 Properties of Exponents THE ZERO POWER WordsNumbers Algebra The zero power of any number except 0 equals 1. 100 0 = 1 (–7) 0 = 1 a 0 = 1, if a  0 Anything to the zero power equals 1

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

14. Course 3 2-7 Properties of Exponents Lesson Quiz: Part 1 Write the product or quotient as one power 3. 8 9 n 7 1. n 3  n 4 10 9 10 5 10 4 4. t 2 5. 2. 8 8 8 t 9 t 7

15. Course 3 2-7 Properties of Exponents 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 = 12 2 items) Lesson Quiz: Part 2 Company A 6.