Lesson 4 6 Zero and Negative Exponents OUR

In this lesson you will learn what a zero or a negative integer means

More Exponents Step 1 Use the division property of exponents to rewrite each of

Notice that some of your answers in Step 1 are positive exponents, some are

Step 2 Go back to the expressions in Step 1 that resulted in

Step 3 Compare your answer from step 2 and Step 1. Tell what

Step 5 Compare your answers from Step 4 and Step 1. Tell what

Step 7 Use what you have learned about negative exponents to rewrite each

$Step 8 In one or two sentences, explain how to rewrite a fraction$

Exponential Form Fraction Form 33 27 32 9 31 3 30 1 3 -1

For any nonzero value of b and for any value of n,

Example B Solomon bought a used car for $5, 600. He estimates that it

Example C Convert each number to standard notation from scientific notation, or vice versa.

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Lesson 4. 6: Zero and Negative Exponents • OUR GOAL: TO WRITE A NUMBER WITH A NEGATIVE EXPONENT IN A FORM THAT HAS A POSITIVE EXPONENT AND WRITE A NUMBER WITH A POSITIVE EXPONENT IN A FORM THAT HAS A NEGATIVE EXPONENT.

In this lesson you will learn what a zero or a negative integer means as an exponent. You will then learn how to manipulate them so you always have positive exponents as your answer.

More Exponents Step 1 Use the division property of exponents to rewrite each of these expression with a single exponent.

Notice that some of your answers in Step 1 are positive exponents, some are negative, and some are zero exponents.

Step 2 Go back to the expressions in Step 1 that resulted in a negative exponent. Write each in expanded form (using the cross out method). Then write the answer as a fraction.

Step 3 Compare your answer from step 2 and Step 1. Tell what a base raised to a negative exponent means. Step 4 Go back to the expressions in Step 1 that resulted in an exponent of zero. Write each in expanded form. Then reduce them.

Step 5 Compare your answers from Step 4 and Step 1. Tell what a base raised to an exponent of zero means.

Step 7 Use what you have learned about negative exponents to rewrite each of these expressions with positive exponents and only one fraction bar.

$Step 8 In one or two sentences, explain how to rewrite a fraction$

Step 8 In one or two sentences, explain how to rewrite a fraction with a negative exponent in the numerator or denominator as a fraction with positive exponents.

Exponential Form Fraction Form 33 27 32 9 31 3 30 1 3 -1 1/3 3 -2 1/9 3 -3 1/27

For any nonzero value of b and for any value of n,

Example B Solomon bought a used car for $5, 600. He estimates that it has been decreasing in value by 15% each year. If his estimate of the rate of depreciation is correct, how much was the car worth 3 years ago? If the car is 7 years old, what was the original price of the car?

Example C Convert each number to standard notation from scientific notation, or vice versa. A pi meson, an unstable particle released in a nuclear reaction, “lives” only 0. 000000026 seconds. The number 6. 67 x 10 -11 is the gravitational constant in the metric system used to calculate the gravitational attraction between two objects that have given masses and are a given distance apart. The mass of an electron is 9. 1 x 10 -31 kg.