1. Laws of Exponents

2. The factors of a power, such as 7 4, can be grouped in different ways. Notice the relationship of the exponents in each product. 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. Additional Example 1: Multiplying Powers with the Same Base 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.

5. Additional Example 1: Multiplying Powers with the Same Base 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. Check It Out: Example 1 A. 4 2 4 4 B. x 4 x 2 Multiply. Write the product as one power.

7. D. p 2 p 2 C. 15 15 2 Check It Out: Example 1 Continued Multiply. Write the product as one power.

8. Notice what occurs when you divide powers with the same base. 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. Subtract exponents. 7 2 7 5 – 3 7 5 7 3 Additional Example 2: Dividing Powers with the Same Base Divide. Write the quotient as one power. A. x 10 x 9 B. Subtract exponents. x 10 – 9 x Think: x = x 1

10. 9 9 9 2 Check It Out: Example 2 Divide. Write the quotient as one power. A. B. n 8 n 5

11. Simplify. Multiply exponents. Additional Example 3: Raising a Power to a Power A. (5 4 ) 2 (5 4 ) 2 5 4 2 5858 B. (6 7 ) 9 (6 7 ) 9 6 7 9 6 63 Multiply exponents.

12. Simplify. Multiply exponents. Additional Example 3: Raising a Power to a Power C. D. (17 2 ) –20 (17 2 ) –20 17 2 –20 17 –40 Multiply exponents. 2323 12–3 2323 12 –3

13. Simplify. Check It Out: Example 3 A. (7 2 ) – 1 B. (7 – 1 ) 2

14. Simplify. Check It Out: Example 3 Continued C. D. (5 –2 ) –3 1515 4–2

15. Additional Example 4: Application The speed of sound at sea level is 3.4029 x 10 2 meters per second. A ship that is 5 kilometers offshore sounds its horn. About how many seconds will pass before a person standing on shore will hear the sound? Write your answer in scientific notation.

16. Write 5 km as meters. Additional Example 4 Continued distance = rate x time It would take about 1.5 x 10 1 seconds for the sound to reach the shore. 5 km = (3.4029 x 10 2 ) x t 5000 = (3.4029 x 10 2 ) x t 5 x 10 3 = (3.4029 x 10 2 ) x t Write 5000 in scientific notation. 3.4029 x 10 2 5 x 10 3 10 2 = t 1.469 x 10 1  t

17. The diameter of a red blood cell is about 7.6 × 10 -4 millimeters. Thai has a slide with a 2-cm drop of red blood cells on it. Approximately how many cells are on the slide? Write your answer in scientific notation. (Hint: Find the ratio of the size of the drop, in millimeters, to the size of one cell.) Check It Out: Example 4