2. Lesson Menu Main Idea Key Concept:Negative Exponents Example 1:Use Positive Exponents Example 2:Use Positive Exponents Example 3:Use Negative Exponents Example 4:Use Negative Exponents Example 5:Perform Operations with Exponents Example 6:Perform Operations with Exponents Example 7:Real-World Example

3. Main Idea/Vocabulary Write expressions using negative exponents.

4. Key Concept

5. Example 1 Use Positive Exponents Write 7 –4 using a positive exponent. Definition of a negative exponent Answer:

6. Example 1 CYP Write 3 –3 using a positive exponent. A. B. C. D.

7. Example 2 Write y –8 using a positive exponent. Use Positive Exponents Definition of a negative exponent Answer:

8. Example 2 CYP Write x –4 using a positive exponent. A. B. C. D.

9. Example 3 Use Negative Exponents Write using a negative exponent. Definition of exponent = 10 –2 Definition of a negative exponent Answer: 10 –2

10. Example 3 CYP A.4 –2 B.2 –4 C.2 –3 D.2 –2 Write using a negative exponent.

11. Example 4 Use Negative Exponents Write using a negative exponent. Definition of exponent = m –9 Definition of a negative exponent Answer: m –9

12. Example 4 CYP A.x –5 B.–x –5 C.x –6 D.–x –6 Write using a negative exponent.

13. Example 5 Perform Operations with Exponents Simplify x 5 x –8. Method 1 Quotient of Powers x 5 x –8 = x 5 + (–8) = x – 3

14. Example 5 Perform Operations with Exponents Answer:x –3 Method 2 Definition of Power

15. Example 5 CYP A.y –26 B.y –6 C.y 26 D.y 6 Simplify y 10 y –16.

16. Example 6 Perform Operations with Exponents Simplify. Method 1 Quotient of Powers = d 3

17. Example 6 Perform Operations with Exponents Answer: d 3 Method 2 Definition of Power

18. Example 6 CYP A.r B.r 7 C.r –1 D.–r –7 Simplify.

19. Example 7 WAVELENGTHS Nanometers are often used to measure wavelengths. 1 nanometer = 0.000000001 meter. Write the decimal as a power of 10. The digit 1 is in the billionths place. Write the decimal as a fraction. 1,000,000,000 = 10 9 Definition of a negative exponent Answer: A nanometer is 10 –9 meter.

20. Example 7 CYP A.10 –10 meter B.10 –11 meter C.10 –12 meter D.10 –15 meter A picometer is a unit of measurement that is even smaller than a nanometer. 1 picometer = 0.000000000001 meter. Write the decimal as a power of 10.