1. Exponent Integers Learn to evaluate expressions with negative exponents.

2. Look for a pattern in the table to extend what you know about exponents to include negative exponents. Start with what you know about positive and zero exponents. ÷10 10 2 1 0 –1 10 –2 10 100 10 1 1 1 1 = 0.1 1 10 1 100 = 0.01

3. 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

4. Evaluate the powers of 10. C. 10 –8 D. 10 –9 10 –8 = = 0.00000001 1 100,000,000 10 –8 = 1 10 10 10 10 10 –9 = = 0.000000001 1 1,000,000,000 10 –9 = 1 10 10 10 10 10 10 10 10 10

5. NEGATIVE EXPONENTS WordsNumbersAlgebra A power with a negative exponent equals 1 divided by that power with it’s opposite exponent. b –n = 1 bnbn 5 –3 = = 1 125 153153 The reciprocal of a number is 1 divided by that number. Remember!

6. 5 –3 Write the reciprocal; change the sign of the exponent. 1 5 5 5 125 1 5 1 3 Evaluate.

7. Bases are the same, so add the exponents. A. 2 –5 2 3 2 –5+3 2 –2 2 2 1 Write the reciprocal; change the sign of the exponent. 1 4 2 2 2 2 2 2 2 2 = 1 4 = Evaluating Products and Quotients of Negative Exponents Evaluate. Check: 2 2 3 = 2 3 = 2 5 1 –5 2 2 3 5

8. Bases are the same, so subtract the exponents. 6 5–8 6 –3 1 6363 Write the reciprocal; change the sign of the exponent. 6565 6868 216 1 Check: 6 5 6 8 6 6 6 6 6 6 6 6 6 6 6 6 6 = Evaluate. B. = 216 1 Evaluating Products and Quotients of Negative Exponents Continued

9. = 5 3 5 2 5 5 5 5 Check: Bases are the same, so subtract the exponents. 5 2–3 5 –1 1 5 1 Write the reciprocal; change the sign of the exponent. 5252 5353 Evaluate. 1 5 5 1 = C.

10. Bases are the same, so add the exponents. 7 –6+7 7 1 7 Evaluate. D. 7 –6 7 7 7 7 = = Check: 7 –6 1 7 6 7 7 7 7 6 7 = 7 7 7 7 7 7 7 7 7 7 = = 7 7 1