Example 1 Using Zero and Negative Exponents a. 5 0

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Example 1 Using Zero and Negative Exponents a. 5 0 Definition of zero exponent 1 = Definition of negative exponent = 5 4 1 b. 5 –4 625 1 = Evaluate power. 2 1 –3 c. = 1 2 3 Definition of negative exponent

Example 1 1 = 1 8 = 8 Using Zero and Negative Exponents Evaluate power. = 8 1 = Divide. 8

A half-life is the amount of time that it takes for a Example 2 Using Negative Exponents SCIENCE A half-life is the amount of time that it takes for a radioactive substance to decay to one half of its original quantity. Suppose radioactive decay causes 400 grams of a substance to decrease grams after 3 half-lives. Evaluate to determine how many grams of the substance are left. 400  2 –3 400  2 –3 SOLUTION  400 2 –3 = 2 3 1 Definition of negative exponent

There are 50 grams left of the substance. Example 2 Using Negative Exponents = 8 1 400 Evaluate exponent. = 50 Simplify. ANSWER There are 50 grams left of the substance.

Evaluate the expression. Guided Practice for Examples 1 and 2 Evaluate the expression. ANSWER 49 1 1. 7 –2 ANSWER 32 1 – ( ) –5 2 – 2. ( ) 0 6 – 3. ANSWER 1 4. 3 1 –2 ANSWER 9

In Example 2, suppose the substance has gone Guided Practice for Examples 1 and 2 WHAT IF? In Example 2, suppose the substance has gone through 4 half-lives. Evaluate to determine how many grams are left.  400 2 –4 5. ANSWER 25 g REASONING Explain why the expression can be used to find the amount of the substance in Example 2 that remains after n half-lives. 6.  400 2 –n ANSWER 2 –n 2 n 1 = , which represents the number of half-lives.