1. Course 3 4-2 Look for a Pattern in Integer Exponents 4-2 Look for a Pattern in Integer Exponents Course 3 Warm Up Warm Up Lesson Presentation Lesson Presentation

2. Course 3 4-2 Look for a Pattern in Integer Exponents 10 7 10 4 Warm Up Evaluate. 1000 1. 10 3 2. 10 0 3. 10 2 10 2 1 10,000 1000 4. 5. 10 6 1

3. Course 3 4-2 Look for a Pattern in Integer Exponents Learn to evaluate expressions with negative exponents and to evaluate the zero exponent.

4. Course 3 4-2 Look for a Pattern in Integer Exponents Look for a pattern in the table to extend what you know about exponents to include negative exponents. ÷ 10 10 2 1 0 –1 10 –2 10 100 10 1 1 1 1 = 0.1 1 10 1 100 = 0.01

5. Course 3 4-2 Look for a Pattern in Integer Exponents Example 1: Using a Pattern to Evaluate Negative Exponents Evaluate the powers of 10. A. 10 –2 10 –2 = 1 10 10 –2 = 1 100 = 0.01 B. 10 –1 10 = = 0.1 –1 1 10 10 = –1 1 10 Extend the pattern from the table. Multiply. Write as a decimal. Extend the pattern from the table. Multiply. Write as a decimal.

6. Course 3 4-2 Look for a Pattern in Integer Exponents Check It Out: 1A Evaluate the powers of 10. 10 –8 10 –8 = 1 100,000,000 10 –8 = 1 10 10 10 10 Extend the pattern from the table. = 0.00000001 Multiply. Write as a decimal.

7. Course 3 4-2 Look for a Pattern in Integer Exponents Check It Out 10 –9 10 –9 = 1 1,000,000,000 10 –9 = 1 10 10 10 10 10 10 10 10 10 Extend the pattern from example 1A. = 0.000000001 Multiply. Write as a decimal.

8. Course 3 4-2 Look for a Pattern in Integer Exponents NEGATIVE EXPONENTS The reciprocal of a number is 1 divided by that number. Remember!

9. Course 3 4-2 Look for a Pattern in Integer Exponents 5 –3 Write the reciprocal; change the sign of the exponent. Example 2: Evaluating Negative Exponents Evaluate. Find the product of three ’s. 1515 Simplify. 5 1 3 = 1 5 5 5 = 125 1 =

10. Course 3 4-2 Look for a Pattern in Integer Exponents 4 –2 Write the reciprocal; change the sign of the exponent. Check It Out: 2A Evaluate. Find the product of two ’s. 1414 Simplify. 4 1 2 = 1 4 = 16 1 =

11. Course 3 4-2 Look for a Pattern in Integer Exponents (–10) –3 Write the reciprocal; change the sign of the exponent. Example 3: Evaluating Negative Exponents Evaluate. Find the product of three ’s. 1 –10 Simplify. 1 = –10 3 1 –10 –10 –10 = –1000 1 = = –0.001

12. Course 3 4-2 Look for a Pattern in Integer Exponents (–7) –4 Write the reciprocal; change the sign of the exponent. Check It Out: 3A Evaluate. Find the product of four ’s. 1 –7 Simplify. 1 = –7 4 1 –7 –7 = 2401 1 =

13. Course 3 4-2 Look for a Pattern in Integer Exponents

14. Course 3 4-2 Look for a Pattern in Integer Exponents Subtract inside the parentheses. Evaluate 5 – (6 – 4) –3 + (– 2) 0. Evaluate the exponents. Example 4: Using the Order of Operations 5 – (6 – 4) –3 + (–2) 0 = 5 – (2) –3 + (–2) 0 = 5 – + 1 1818 = 5 7878 Add and subtract from left to right.

15. Course 3 4-2 Look for a Pattern in Integer Exponents Subtract inside the parentheses. Evaluate 3 + (7 – 4) –2 + (–8) 0. Evaluate the exponents. Check It Out: 4A 3 + (7 – 4) –2 + (–8) 0 = 3 + (3) –2 + (–8) 0 = 3 + + 1 1919 = 4 1919 Add.

16. Course 3 4-2 Look for a Pattern in Integer Exponents Lesson Quiz Evaluate the powers of 10. 1. 10 –3 0.001 2. 10 –7 0.0000001 Evaluate. 3. (–6) –2 4. 4 2 –3 +10 –1 5. 8 0 –(11 – 2 4 ) –2 1 36 3535 24 25 6. (4w) –2 + w –1 for w = 4 65 256