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Simplify Expressions and Solve Real-World Problems

Learn how to simplify expressions using properties and solve real-world problems. Examples include simplifying expressions with powers and finding the total number of bees in a study.

michaeltidwell
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Simplify Expressions and Solve Real-World Problems

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  1. (24 13)8 = 248 138 a. b. c. d. (–4z)2 = (–4 z)2 = (–4)2z2 = 16z2 (9xy)2 = (9 x y)2 = 92x2y2 = 81x2y2 – (4z)2 = – (4 z)2 = – (42z2) = –16z2 EXAMPLE 3 Use the power of a product property

  2. (2x3)2x4 = 22 (x3)2x4 = 4 x6x4 (2x3)2x4 EXAMPLE 4 Use all three properties Simplify Power of a product property Power of a power property = 4x10 Product of powers property

  3. EXAMPLE 5 Solve a real-world problem BEES In 2003 the U.S. Department of Agriculture (USDA) collected data on about 103 honeybee colonies. There are about 104 bees in an average colony during honey production season. About how many bees were in the USDA study?

  4. ANSWER The USDA studied about 107, or 10,000,000, bees. EXAMPLE 5 Solve a real-world problem SOLUTION To find the total number of bees, find the product of the number of colonies, 103, and the number of bees per colony, 104. 103 104 = 103+4 = 107

  5. (42  12)2 9. (–3n)2 10. 11. (9m3n)4 5  (5x2)4 12. for Examples 3, 4 and 5 GUIDED PRACTICE Simplify the expression. = 422 122 = 9n2 = 6561m12n4 = 3125x8

  6. 13. WHAT IF? In Example 5,102 honeybee colonies in the study were located in Idaho. About how many bees were studied in Idaho? ANSWER about 1,000,000, bees for Examples 3, 4 and 5 GUIDED PRACTICE

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