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Name Class 7-5 Date Practice Form G Division Properties of Exponents Simplify each expression. 1. 56 52 2. 55 52 3. x7 x4 4. m 3 m 5 6. 21m8 3m 2 x6 y9 5. 2 5 x y 3 7. 5 9. 4 4 7 3x 8. 2y 2 11. 12 p 10. 15 p 13. 3 4 3 x 2 y 5 z 2 5 5 xz 12. 3 3 3x 4 5 2y ab3 5 a b 3 2 4m 3n 2m mn 2 14. 3 5 3 Explain why each expression is not in simplest form. 15. 24r3 16. (3x)2 17. m3n0 18. y5 y Simplify each quotient. Write each answer in scientific notation. 19. 6 20. 4.5 10 5 102 3.6 107 1.5 103 Prentice Hall Gold Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 43 Name Class 7-5 Date Practice (continued) Form G Division Properties of Exponents 3 64 21. Error Analysis A student simplifies the expression 2 as follows: 3 3 64 42 3 2 3 2 [(6 3) ] (2 ) 64. What mistake did the student make in 3 simplifying the expression? What is the correct simplification? 22. 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. 23. The area of a triangle is 80x5 y 3. The height of the triangle is x4 y. What is the length of the base of the triangle? 3 12 m5 24. Open-Ended First simplify the expression by raising each factor in 15m 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? Prentice Hall Gold Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 44