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.

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Presentation transcript:

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.

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

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

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 x -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

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.

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

GUIDED PRACTICE for Examples 3 and –2 = (–2) –5 = 1 32 –

GUIDED PRACTICE for Examples 3 and 4 = –3

GUIDED PRACTICE for Examples 3 and 4 = –5 10 5

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

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

GUIDED PRACTICE for Examples 3 and 4 = 10 a a – 3 a4a4