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Name: Review for Mid-Unit B Test Date: Class: Multiple Choice For each of the following questions choose the best answer. 1. Write the expression (7) (7) (7) x x x y in exponential form. A. 7 3 x 3 C. (7) 3 x 3 y B. (7) 3 x 3 y D. 7xy 4 2. Find n so that the equation is true: (53 ) n 518 A. n 6 B. n 15 C. n 13 D. Infinite Solution 3. Find m and n so that the equation is true: 3 m 6 5 3 4 6 n 38 610 A. m 2, n 2 B. m 3, n 5 C. m 4, n 2 D. m 4, n 5 4. Using the rules of exponents, simplify the following expression. Your answer should be in exponential form. 7 3 56 7 52 A. 7 3 5 2 B. 7 4 5 3 C. 7 2 5 4 D. 7 3 5 4 5. Using the rules of exponents, simplify the following expression. Your answer should be in exponential form. 4 3 2 2 1 1 2 3 4 4 3 A. 7 2 1 3 4 5 B. 7 2 1 3 4 5 C. 3 2 12 12 D. 4 144 12 Review for Mid-Unit B Test 6. Using the rules of exponents, simplify the following expression. Your answer should be in exponential form. 2m 2n A. 2 m n B. C. 4 m n 2 mn D. Not enough information is provided 7. Simply the expression ((3) 3 ) 4 A. (3)12 B. 312 C. (3) 7 D. 3 7 12 2 7 2 2 7 8. Simplify the following expression: 2 A. 7 10 2 B. 7 6 2 C. 7 9. Which of the following is equivalent to A. 5 3 5 B. 15 15 5 10 2 D. 7 6 5 5 33 3 4 ? 510 32 C. 5 5 35 D. 3 5 5 2 Review for Mid-Unit B Test 10. Which of the following is NOT equivalent to A. w5 w5 B. w 0 w5 ? (Choose one) w w4 C. 1 D. 0 11. Which of the answers in question 10 is the equivalent expression in simplest form. #12 to #15 You Pick Two Multiple Choice For each of the following questions pick two answers that are true. 12. Which of the following is equivalent to A. x 57 B. x 75 C. 1 x 2 D. 13. Which of the following is equivalent to A. 13 2 B. 1 13 2 x5 x7 1 x2 13 9 ? 13 7 C. 139 ( 7 ) D. 13 9 7 2 2 14. Which of the following is NOT equivalent to y 3 ? 5 2 2 6 y 5 A. 4 5 y 25 B. C. 4 y6 25 15. Which of the following are equivalent to the expression: A. w 5 z 13 w z 2 6 B. w z 11 C. z 11 w 2 2 5 y 5 D. w 5 z 13 z 6 w2 D. w 3 z 7 3 Review for Mid-Unit B Test Short Answer: 16. Write the expression k 7 w5 in simplest form. k 3 w4 17. Write the expression k 3 w9 in simplest form using only positive exponents. k 7 w4 18. Write the expression 10 z 7 using only positive exponents. 19. Simplify the expression m 7 using only positive exponents. 2m 5 Multiple Answer For each of the following questions check the box for each of the answers that apply. 20. Determine which of the following expressions are equivalent to the expression below. (Choose three answers) w5 z 6 z 6 w5 A. C. E. z6 z6 wz 11 wz 11 B. w5 w5 D. 1 0 4 Review for Mid-Unit B Test 21. Determine which of the following expressions are equivalent to the following expression. (Choose three answers) 4 x 3 (2 x 4 x 2 ) A. 8 x12 x 2 B. 8 x 7 ( x 2 ) C. 8x 14 D. 8 x 7 x 2 E. 8x 9 F. 8 x 7 4 x 5 22. Determine which of the following expressions are NOT equivalent to the expression: (Choose three answers) 4 x 2 7 x 3 1 28 x 5 A. 28x 6 B. C. 28 x5 D. 28 x 5 E. 1 28 x 6 Short Answer For each of the following questions show your work and give your final answer in the space provided. 23. Use the expression (5) x to complete the following: If x = 3, write the expression in expanded form, Simplify the expression that you wrote in the previous bullet. List three values of x for which the simplified expression will be positive. List three values of x for which the simplified expression will be negative. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ 5 Review for Mid-Unit B Test 24. Kelly wrote that 2 4 25 2 20 Complete the following. Explain Kelly’s mistake. Support your answer with written or mathematical reasoning. Write an exponential expression using a base of 2 and exponents of 4, 5, and 20 that would make her answer correct. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ 25. Write an equation to find the value of x that makes (3) 3 x 2 (3) 2 x 1 (3) 3 x3 Equation: Solve the equation that you wrote: Check your answer by substituting the value that you found for x and checking to see that both sides of the equation are equal. 26. Write an equation to find the value of x that makes (7) 5 x 3 (7)12 2x (7) Equation: Solve the equation that you wrote: Check your answer by substituting the value that you found for x and checking to see that both sides of the equation are equal. 315 3 3 as a single term of the form 3 n , where n is an 5 7 3 3 integer. Show your work. 27. Rewrite the expression 6