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Using a Negative Exponent

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?. 1. 1 microsecond is equal to. second. 1,000,000. EXAMPLE 1. Using a Negative Exponent. SOLUTION.

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Using a Negative Exponent

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  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? 1 1 microsecond is equal to second. 1,000,000 EXAMPLE 1 Using a Negative Exponent SOLUTION The flash lasts 1 microsecond. Because the prefix micro means one millionth of a unit, you know that

  2. 1 1 = 1,000,000 106 = 10– 6 ANSWER One flash of the strobe light lasts about 10 – 6second. EXAMPLE 1 Using a Negative Exponent Write1,000,000as106. Definition of negative exponent

  3. 52 5– 5 1 = 53 1 = 125 EXAMPLE 2 Evaluating a Numerical Expression Evaluate the expression. = 5 2 + (– 5) Product of powers property Simplify. = 5– 3 Definition of negative exponent Evaluate the power.

  4. 8 8x-3 8 • x-3 x1 x x4 – 2 • 1 = a. – 2n0 b. = – 2 = EXAMPLE 3 Simplifying Variable Expressions Simplify. Write the expression using only positive exponents. = – 2 •n0 Zero exponent applies only to n. Definition of zero exponent Multiply. Exponent applies only to x = 8 •x-3-1 Quotient of powers property = 8 •x-4 Subtract exponents. Definition of negative exponent

  5. for Examples 3 and 4 GUIDED PRACTICE 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. ANSWER One flash of the strobe light lasts about 103 second. for Examples 3 and 4 GUIDED PRACTICE

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

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

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

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

  11. 7. b2b–2 1 = 5x4 8. x –7 for Examples 3 and 4 GUIDED PRACTICE = 5x11

  12. 10a– 3 9. a4 10 = a7 for Examples 3 and 4 GUIDED PRACTICE

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