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Name Class Date Practice Form G Division Properties of Exponents Simplify each expression. 56 1. 2 625 5 5 55 2. 2 5 1 x8 3. 3 x 4 4. x8 6. 4 3 7.a 5 b 81 3 49 16 12p2 11. ° ¢ 15p 13. a -4 m2 625 3x2y 5z -2 -3 125z 21 b 5xz 5 27x 3y 15 7m 2 1 3m4 10. a- 2 256p 1 21m4 3x 8. a 2y b 625 -2 m-3 m-5 3 x6 y 9 5. 2 5 x 4y 4 x y 9.a 4 7b 125 3 3x4 b 2y 5 ab3 12. a 5 b a b 14. 27x 3 8y 3 -3 8y 15 27x 12 -2 a8 b4 (4m2) (3n5) −6m2n2 (2m-3) ( - mn)3 Explain why each expression is not in simplest form. 15. 24 r 3 16. (3x)2 24 is not simplified both factors should be squared y5 18. y 17. m3 n0 n0 = 1, so m3n0 = m3 y5 4 y can be simplified to y Simplify each quotient. Write each answer in scientific notation. 19. 3.6 * 107 2.4 × 104 1.5 * 103 20. 4.5 * 10-6 9.0 × 10−5 5 * 10-2 Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. Name Class Date Practice (continued) Form G Division Properties of Exponents 21. Writing Explain how you divide expressions with numerators and denominators written in scientific notation. How do you handle the exponents? What do you do with the coefficients? Connect your response to the rules you have learned regarding the division properties of exponents. For expressions with numerators and denominators in scientific notation, you work separately with the numerical parts and the powers of 10. To divide powers of 10, subtract the exponents. Put the answer back into scientific notation form. 22. A computer can do a computation in 6.8 * 10-9 seconds. How many computations can the computer do in 5 minutes? 4.41 × 1010 3 64 23. Error Analysis A student simplifies the expression a 2 b as follows: 3 3 64 4-2 3 2 3 a 2 b = [(6 , 3) ] = (2 ) = 64. What mistake did the student make in 3 simplifying the expression? What is the correct simplification? The student should have expanded the powers inside the brackets first to follow ( # ## # ) 6 6 3 = (2 the order of operations. 6 6 3 3 # 2 # 6 # 6)3 = 1443 = 2,985,984 24. Reasoning The division property of exponents says that to simplify powers with the same base you subtract the exponents. Use examples to show why powers need to have the same base in order for this technique to work. Answers may vary. Sample: 65 =6 63 65 =6 33 # 6 # 6 # 6 # 6 = 6 # 6 = 36: 65 = 65−3 = 62 = 36; same 6 # 6 # 6 63 # 6 # 6 # 6 # 6 = 6 # 6 # 2 # 2 # 2 = 288: 65 = ( 6 )2 = 22 = 4; different 3 # 3 # 3 3 33 same base = same answer; different bases = different answers; The division property works only with numbers with the same bases. 25. The area of a triangle is 80x 5 y 3 . The height of the triangle is x4 y. What is the length of the base of the triangle? 160xy 2 3 12m5 26. Open-Ended First simplify the expression a 15m b by raising each factor in the parentheses to the third power and next reducing the result. Then simplify by some other method. Explain your method. Are the results the same? Which method do you prefer? 5 3 ( 12m 15m ) = 15 12 (12m5)3 ; = 1728m 3 = 64m 125 (15m)3 3375m 5 3 ( 12m 15m ) 3 ( ) 4 = 4m 5 12 Simplifying = 64m 125 within the parantheses first and then raising each factor to the thrid power gives the same results. I prefer this method because the numbers are easier to calculate. Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.