1. Using a Negative Exponent EXAMPLE 1 Strobes The picture of the golf ball was taken using a strobe light. Each flash of the strobe light lasted about 1 microsecond. How can you write this time in seconds as a power of ten? SOLUTION The flash lasts 1 microsecond. Because the prefix micro means one millionth of a unit, you know that 1 microsecond is equal to 1 1,000,000 second.

2. Using a Negative Exponent EXAMPLE 1 1 1,000,000 = 10 6 1 Write 1,000,000 as 10 6. =10 – 6 Definition of negative exponent One flash of the strobe light lasts about 10 – 6 second. ANSWER

3. Evaluating a Numerical Expression EXAMPLE 2 Evaluate the expression. Product of powers property = 5 – 3 Simplify. = 1 5353 Definition of negative exponent = 1 125 Evaluate the power. = 5 2 + (– 5) 5 2 5 – 5

4. Simplifying Variable Expressions EXAMPLE 3 Zero exponent applies only to n. Definition of zero exponent Multiply. Simplify. Write the expression using only positive exponents. a.a. – 2n 0 – 2 1 == – 2 = – 2 n 0 = 8 x -3-1 8x -3 x b.b. Quotient of powers property Subtract exponents. = 8 x -3 x1x1 Exponent applies only to x = 8 x -4 8 x4x4 Definition of negative exponent

5. GUIDED PRACTICE for Examples 3 and 4 1. What If ? In Example 1, suppose the flash of a light lasted about one thousandth of a second. Write this time in seconds as a power of 10.

6. GUIDED PRACTICE for Examples 3 and 4 ANSWER One flash of the strobe light lasts about 10 3 second.

7. GUIDED PRACTICE for Examples 3 and 4 2.7 –2 = 1 49 3. (–2) –5 = 1 32 –

8. GUIDED PRACTICE for Examples 3 and 4 = 1 36 4.6 6 –3

9. GUIDED PRACTICE for Examples 3 and 4 = 1 5.5. 10 –5 10 5

10. GUIDED PRACTICE for Examples 3 and 4 6.6. –6m –1 = –6 m Simplify. Write the expression using only positive exponents.

11. GUIDED PRACTICE for Examples 3 and 4 = 1 7.b 2 b –2 8. 5x45x4 x –7 = 5x 11

12. GUIDED PRACTICE for Examples 3 and 4 = 10 a 7 9. 10a – 3 a4a4