1. Warm Up California Standards Lesson Presentation Preview

2. Warm Up Simplify. 1000 1. 10 3 2. 10 1 3. 10 4 10 10,000 100,000 4. 5. 1,000,000 10 5 10 6

3. NS2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base. AF2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents. California Standards

4. Look at the pattern shown in the table to extend what you know about exponents to include negative exponents. ÷ 10 ÷ 10 ÷ 10 ÷ 10 10 2 10 1 10 0 10 – 1 10 – 2 10 • 10 100 10 10 1 1 1 10 1 10 = 0.1 1 10 • 10 1 100 = 0.01

5. Notice from the chart that as the exponents decrease by 1, the value of the expression decreases by a factor of 10. ÷ 10 ÷ 10 ÷ 10 ÷ 10 10 2 10 1 10 0 10 – 1 10 – 2 10 • 10 100 10 10 1 1 1 10 1 10 = 0.1 1 10 • 10 1 100 = 0.01

6. Additional Example 1: Using a Pattern to Evaluate Negative Exponents Simplify the powers of 10. A. 10 –2 B. 10 –1 Multiply. Write as a decimal. Multiply. Write as a decimal. 10 –2 = 1 10 • 10 = 1 100 = 0.01 = = 0.1 1 10 10 = – 1 1 10

7. Check It Out! Example 1A Simplify the powers of 10. 10 –8 Extend the pattern from the table. = 0.00000001 Multiply. Write as a decimal. = 1 100,000,000 10 –8 = 1 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10

8. Check It Out! Example 1B 10 –9 Extend the pattern from Example 1A. = 0.000000001 Multiply. Write as a decimal. Simplify the powers of 10. = 1 1,000,000,000 10 –9 = 1 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10

9. NEGATIVE EXPONENTS

10. 5 –3 Write the power under 1; change the sign of the exponent. Additional Example 2A: Evaluating Negative Exponents Simplify. Simplify. Find the product. 1 5 • 5 • 5 = 125 1 =

11. (–10) –3 Write the power under 1; change the sign of the exponent. Additional Example 2B: Evaluating Negative Exponents Simplify. Simplify. = –0.001 Find the product. 1 – 10 • –10 • –10 = – 1000 1 =

12. 4 –2 Write the power under 1; change the sign of the exponent. Check It Out! Example 2A Simplify. Simplify. Find the product. 1 4 • 4 = 16 1 =

13. (–7) –4 Write the power under 1; change the sign of the exponent. Check It Out! Example 2B Simplify. Simplify. Find the product. 1 – 7 • –7 • –7 • –7 = 2401 1 =

15. Subtract inside the parentheses. Simplify 5 – (6 – 4) –3 + (–2) 0 . Rewrite 2 -3 . Additional Example 3: Using the Order of Operations 5 – (6 – 4) –3 + (–2) 0 5 – (2) –3 + (–2) 0 Add and subtract from left to right. Simplify the powers. 5 7 8 5 – + 1 1 2 3 5 – + 1 1 8

16. Subtract inside the parentheses. Simplify 3 + (7 – 4) –2 + (–8) 0 . Rewrite 3 -2 . Check It Out! Example 3 3 + (7 – 4) –2 + (–8) 0 3 + (3) –2 + (–8) 0 Simplify the powers. Add. 4 1 9 3 + + 1 1 9 3 + + (–8) 0 1 3 2

17. Lesson Quiz Simplify the powers of 10. 1. 10 –3 0.001 2. 10 –7 0.0000001 Simplify. 3. (–6) –2 4. 4 • 2 –3 +  10 –1 5. 8 0 –  (11 – 2 4 ) –2 1 36 3 5 24 25 6. Evaluate (4 w ) –2 + w –1 for w = 4. 65 256