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. Lesson 4.6: Zero and Negative Exponents

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 with a negative exponent in the numerator or denominator as a fraction with positive exponents.

Exponential FormFraction Form / / /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 seconds.  The number 6.67 x 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 kg.

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 seconds.  The number 6.67 x 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 kg.