Chapter4.2
- 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
- 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