Identify the exponent and the base in the expression 138. Skills Check Identify the exponent and the base in the expression 138. 2. x2 when x = 10 3. = 3 a3 when a 4. = 1.2 m2 when m

Standards: Objectives: 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. Objectives: Use the product of powers property Use the power of a power property Use the power of a product property Use all three properties

What is the expanded form of 23

Example 1 a. • ( ) 2 5 – 2 3 = ( ) 2 3 5 – + ( ) – 2 8 = b. • x4 x3 = Use the product of powers property a. • ( ) 2 5 – 2 3 = ( ) 2 3 5 – + ( ) – 2 8 = b. • x4 x3 = x4 3 + = x7 c. • 76 7 78 = • 71 78 76 = 6 1 8 7 + = 715

Example 1 d. • y y3 y2 = • y3 y2 y1 = 1 3 2 y + = y6 Use the product of powers property d. • y y3 y2 = • y3 y2 y1 = 1 3 2 y + = y6

Simplify the expression. Guided Practice for Example 1 Simplify the expression. 1. 32 • 37 2. ( ) 5 – • 5 9 3. • z5 4. • x6 x x2

Multiple Choice Practice Example 2 Multiple Choice Practice Which expression is equivalent to w3w2? w3w3 w4w w5w w9w4 SOLUTION STEP 1 Simplify the given expression, w3w2. w3w2 3 2 w = + w5 STEP 2 Determine which expression equals . 5 w w3w3 3 3 = + Choice A: w6

Multiple Choice Practice Example 2 Multiple Choice Practice Choice B: w4w = w4w1 = w = w5 4 1 + ANSWER The correct answer is B. 9

[ ] Use the power of a power property Example 3 a. ( ) 2 3 5 = 25 3 • 25 3 • = 215 = ( ) 2 5 6 – • b. ( ) [ ] 2 6 – 5 = ( ) 6 – 10 c. ( ) x 4 2 = x2 4 • = x8 11

[ ] Use the power of a power property Example 3 = ( ) 2 + y 6 2 • d. ( 6 2 • d. ( ) [ ] 6 2 + y = 12 ( ) 2 + y 12

[ ] for Examples 2 and 3 Guided Practice Simplify the expression. 5. m • m 8 9 6. ( ) 4 2 7. ( ) [ ] 4 2 – 5 8. ( ) x 7 5

Example 4 a. ( ) 24 13 • 8 = 248 138 • b. ( 9xy ) 2 81x2y2 = ( 9 ) 2 • Use the power of a product property a. ( ) 24 13 • 8 = 248 138 • b. ( 9xy ) 2 81x2y2 = ( 9 ) 2 • x y 92 x2 y2 c. ( 4z ) 2 – = 16z2 ( 4 ) 2 • – z z2 ( 4z ) 2 – d. = 42 • z2 – ( ) 16z2 4 z 2

Example 5 Simplify ( ) 2x 2 x4. 3 • ( ) 2x3 2 = x4 22 • x 3 = 4 • x6 Use all three properties Simplify ( ) 2x 2 x4. 3 • ( ) 2x3 2 = x4 22 • x 3 Power of a product property = 4 • x6 x4 Power of a power property = 4x10 Product of powers property

Simplify the expression. Guided Practice for Examples 4 and 5 Simplify the expression. 9. ( ) 42 12 • 2 10. ( ) 3n – 2 11. ( 9m n ) 4 3 12. ( 5x ) 4 2 5 •

In 2003 the U.S. Department of Agriculture (USDA) Example 6 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? 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 3 4 10 = + 107 18

The USDA studied about 107 , or 10,000,000 bees. Example 6 Solve a real-world problem ANSWER The USDA studied about 107 , or 10,000,000 bees.

Guided Practice for Example 6 13. WHAT IF? In Example 6, about 102 honeybee colonies in the study were located in Idaho. About how many bees were studied in Idaho?

Evaluate the expression. Skills Check Evaluate the expression. r2 when r 7. = 6 5 z3 when z 8. = 2 1 Evaluate the expression. 9. 81 10. 64 –

Evaluate the expression. Skills Check Evaluate the expression. 100 11. – + – 12. 121 Use the distributive property to write an equivalent expression. 13. ( ) 3 – y 4 14. ( ) 2 – x

Use the distributive property to write an equivalent expression. Skills Check Use the distributive property to write an equivalent expression. 15. – x ( x + 11 ) 16. ( ) 9 – x 4x

Standards: Objectives: 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. Objectives: Use the product of powers property Use the power of a power property Use the power of a product property Use all three properties