Lesson 1.2 The Product and the Quotient of Powers
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- Eleanore Parsons
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1 Lesson. The Product and the Quotient of Powers Use the product of powers property to simplify numerical expressions. a) Use the product of powers property. b) () 3 () 7 () 3 () 7 () 3 7 () 0 0 Use the product of powers property. Simplify the exponent. c) Use the product of powers property Use the of powers property. Reteach Course 3A 9
2 . (7) (7) (7) (7) Use the of powers property. Simplify the exponent Use the of powers property () 3 () Chapter Lesson.
3 Use the product of powers property to simplify algebraic expressions. a) a? a 3 a? a 3 a 3 Use the product of powers property. b) (f ) 4? (f ) a (f ) 4? (f ) (f ) 4 Use the product of powers property. (f ) 6 Simplify the exponent. c) (9p) 0? (9p) 0 f 6 (9p) 0? (9p) (9p) Use the product of powers property. (9p) 0 8. b b 6 b b 6 Use the of powers property. 9. (q) 3 (q) 3 (q) 3 (q) 3 Use the of powers property. Simplify the exponent. 0. (4s) 8 (4s) (4s) 8 (4s) Use the of powers property. Reteach Course 3A
4 . w? w. (k) 4? (k) 3. (0t)? (0t) 4 Use the product of powers property to simplify algebraic expressions. a) a b 3? a 3 b a b 3? a 3 b a? b 3?a 3? b a? a 3?b 3? b a 3? b 3 a b b) 4p q 4? p 4 q 6 4p q 4? p 4 q 6 4? p? q 4?? p 4? q 6 4?? p? p 4? q 4? q 6 8? p 4? q 4 6 8p 6 q 0 Rewrite the product. Regroup factors with the same base. Add the exponents of the factors with the same base. Rewrite the product. Regroup numbers, and regroup factors with the same bases. Add the exponents of the factors with the same base. Chapter Lesson.
5 4. x y? x 4 y 3 x y? x 4 y 3??? the product.??? Regroup the factors with the base.? the exponents of the factors with the same base.. c 4 d c d 6 6. j 3 k 3j k 7 Use the quotient of powers property to simplify numerical expressions. a) Use the quotient of powers property. 3 3 b) () 8 4 () 4 () 8 4 () 4 () 8 4 Use the quotient of powers property. () 4 Simplify the exponent. 4 c) Use the quotient of powers property..3 7 Reteach Course 3A 3
6 Use the of powers property. 8. (4) 7 4 (4) 3 (4) 7 4 (4) 3 Use the of powers property. Simplify the exponent Use the of powers property (6) 4 4 (6) Chapter Lesson.
7 Use the quotient of powers property to divide algebraic expressions. a) q 4 4 q 3 q 4 4 q 3 q 4 3 Use the quotient of powers property. b) (p) 3 4 (p) q (p) 3 4 (p) (p) 3 Use the quotient of powers property. (p) Simplify the exponent. p 4. x 9 4 x 7 x 9 4 x 7 Use the of powers property.. (r) 4 (r) (r) 4 (r) Use the of powers property. 6. y 4 4 y 7. (a) 0 4 (a) 4 Reteach Course 3A
8 Use the quotient of powers property to simplify algebraic expressions. a) u s 6 4 u 3 s 4 u s 6 4 u 3 s 4 u s 6 u 3 s 4 u u? s 6 3 s 4 Write the quotient as a fraction. Rewrite the fraction as a product of two fractions. b) 6a 6 b 4 8a 3 b u 3? s 6 4 Use the quotient of powers property. u s 6a 6 b 4 8a 3 b 6a6 b 8a 3 b 6 8? a6 a 3? b b Write the quotient as a fraction. Rewrite the fraction as a product of three fractions.? a 6 3? b Use the quotient of powers property. a 3 b 8. e 7 f 8 4 e 3 f 4 e 7 f 8 4 e 3 f 4 Write the quotient as a.? Rewrite the fraction as a of two fractions.? Use the of powers property. 6 Chapter Lesson.
9 9. 8x 4 y 7 4 7x 3 y 8x 4 y 7 4 7x 3 y Write the quotient as a.?? Rewrite the fraction as a of three fractions.?? Use the of powers property. 30. w 9 v 6 z 4 4 w v 3 z d 0 g 8 4 3d 7 g 3. c 4 m 9 p 4 c m p k m k 6 m Reteach Course 3A 7
10 Use exponent properties to simplify numerical and algebraic expressions. a) Use the product of powers property Use the quotient of powers property. 3 8 b) Use the product of powers property. 9 Use the quotient of powers property. 3 8 Chapter Lesson.
11 c) a 3a 4a 3 4 a 3a a a a a a a a a 3a 4a a 3a a 4a a 6 3 Regroup the numbers, and regroup the factors with the same bases. 3 4 Use the product of powers property. 8 a 9 a 8 a ( 9 ) Use the quotient of powers property. 8 a Use the of powers property. Use the of powers property. Reteach Course 3A 9
12 3. (0.3) (0.3) (0.3) (0.3) (0.3) (0.3) (0.3) (0.3) (0.3) 3 (0.3) (0.3) (0.3) Use the of powers property. Use the of powers property. 36. x 8x 8x x 6x 3x x 8x 8x 7 Regroup the numbers, and regroup the x 6x 3x factors with the same bases. Use the of powers property. Use the of powers property p p 0p p 3p p Chapter Lesson.
13 Solve a real-world problem in exponential notation. Heather extracted microliter of blood sample from a vile containing 00 microliters of blood. The sample she extracted contained approximately 0 6 red blood cells. Predict how many red blood cells were initially in the vile of blood? Write your answer in exponential notation. Number of red blood cells in vile Number of red blood cells in microliter of blood sample? Number of liters of blood sample 0 6? 00 Substitute values. 0 6? 0 Rewrite 00 as Use the product of powers property. 0 8 There were approximately 0 8 red blood cells in the vile of blood. Solve. Show your work. 39. A grain of sand has a mass of approximately 0 milligrams. A rock has a mass of approximately 0 0 milligrams. How many times more is the mass of the rock than the mass of the grain of sand? 40. There are approximately 0 4 blueberries in one crate. In a particular week, a blueberry farm sold,000 crates of blueberries. How many blueberries were sold in that week? Write your answer in exponential notation. Reteach Course 3A
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