Study Guide and Intervention Extending the pattern below shows that = or. 2 0 This suggests the following definition. a n = a n, for a 0 and any integer n. Example a. 3 b. y 2 3 3 y 2 y 2 We can evaluate algebraic expressions with negative exponents using the definition of negative exponents. Example 2 Evaluate b 2 if b 3. b 2 3 2 Replace b with 3. 3 2 9 Find 32. Definition of negative exponent Exercises. 2. ( 7) 8 ( 7) 8 3. b b. n n or n Write each fraction as an expression using a negative exponent other than. 5. 2 2 2 2. 3 3 7. 5 2 5 2 8. 9 7 2 Evaluate each expression if m, n, and p. 9. p 2 3 0. m 3. (np) 2. 3m 8 Glencoe/McGraw-Hill 95 Glencoe Pre-Algebra
Skills Practice. 3 3 2. 8 7 8 7 3. 0 0. ( 2) ( 2) 5. ( 0) 3 ( 0) 3. ( 7) 2 ( 7) 2 7. n 0 n 0 8. b 8 b 8 9. q 5 q 5 0. m m. v v 2. p 2 p 2 Write each fraction as an expression using a negative exponent other than. 3. 8 2 8 2. 0 5 0 5 5. 2 3 2 3. 7 7 7. 7 7 8. 2 2 2 2 9. 3 7 3 7 20. 9 2 9 2 2. 3 2 3 2 22. 2 2 23. 5 2 2. 2 5 3 2 Evaluate each expression if x, y 2, and z 3. 25. y z 8 2. z 2 9 27. x 8 28. y 5 3 2 29. z 3 30. y 2 7 2 3. z 32. 5 z 8 25 33. x 99 3. z 35. z 3. y z 8 Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra
Practice. 7 8 7 8 2. 0 0 3. 23 2 3. ( 5) 2 ( 5) 2 5. ( 8) 0 ( 8) 0. m 99 99 m 7. ( ) 2 ( ) 2 8. c c 9. p 5 p 5 0. g 7 g 7. 5z 5 z 2. 3t 3 t Write each fraction as an expression using a negative exponent. 3. 2 0 2 0. 2 9 3 29 3 5.. 39 7. 3 9 8 7 8 7 8. m 9. x 3 20. x 3 a 2 a 2 2. 9 m 7 2 22. 8 2 3 23. 2 2 2. 3 2 9 Evaluate each expression if x 3, y 2, and z. 25. x 8 2. y 2 27. y 5 3 2 28. z 2 5 29. 5 y 30. 0 y 2 5 00 3. 3z 3 32. zy 33. (xz) 2 3. HAIR Hair grows at a rate of inch per day. Write this number using negative exponents. 8 2 or 3 or 2 Glencoe/McGraw-Hill 97 Glencoe Pre-Algebra
Answers () Study Guide and Intervention Extending the pattern below shows that = or. 2 5 5 0 5 2 5 This suggests the following definition. a 2 n = a n, for a 0 and any integer n. Example a. 3 2 b. y 2 2 3 2 5 3 y 2 2 5 y 2 We can evaluate algebraic expressions with negative exponents using the definition of negative exponents. Example 2 Evaluate b 2 if b 3. b 2 2 5 3 2 2 Replace b with 3. 5 3 2 Definition of negative exponent 5 9 Find 32. Exercises. 2 2. (2 7) 2 8 ( 7) 8 3. b 2 b. n 2 n or n Write each fraction as an expression using a negative exponent other than. 5. 2 2 2 2. 3 3 7. 2 5 2 8. 5 9 7 2 Evaluate each expression if m, n, and p. 9. p 2 2 3 0. m 2 3. (np) 2. 3m 8 Glencoe/McGraw-Hill 95 Glencoe Pre-Algebra Skills Practice. 3 2 3 2. 8 2 7 8 7 3. 0 2 0. (2 2) 2 ( 2) 5. (2 0) 2 3 ( 0) 3. (2 7) 2 2 ( 7) 2 7. n 2 0 n 0 8. b 2 8 b 8 9. q 2 5 q 5 0. m 2 m. v 2 v 2. p 2 2 p 2 Write each fraction as an expression using a negative exponent other than. 3. 8 2 8 2. 0 0 5 5 5. 2 3 2 3. 7 7 7. 7 7 8. 2 2 2 2 9. 3 7 3 7 20. 9 2 9 2 2. 3 2 3 2 22. 2 2 23. 2 5 5 2 2. 3 2 Evaluate each expression if x, y 2, and z 3. 25. y 2 z 8 2. z 2 2 9 27. x2 8 28. y 2 5 3 2 29. z2 3 2 7 30. y2 2 3. z 2 8 32. 5 z 25 33. x2 99 3. z 35. z 3. y z 8 Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra Answers Glencoe/McGraw-Hill A7 Glencoe Pre-Algebra
Answers () Practice. 7 2 8 7 8 2. 0 2 0 3. 232 2 3. (2 5) 2 2 ( 5) 2 5. (2 8) 2 0 ( 8) 0. m 2 99 m 99 7. (2 ) 2 2 ( ) 2 8. c 2 c 9. p 2 5 p 5 0. g 2 7 g 7. 5z 2 5 z 2 2. 3t 2 3 t 2 Write each fraction as an expression using a negative exponent. 3. 2 0 2 0. 2 9 29 3 3 5.. 3 39 7. 9 8 8 7 7 8. m m 9. x x 3 20. 3 a 2 a 2 2. 7 2 9 22. 8 2 3 23. 2 2 2. 9 3 2 Evaluate each expression if x 3, y 8 2, and z. 25. x 2 27. y2 5 2. y2 2 27. y2 5 3 2 28. z 2 2 5 29. 5 y 2 5 30. 0 y 00 3. 3z 2 3 32. zy 33. (xz) 2 2 3. HAIR Hair grows at a rate of inch per day. Write this number using negative exponents. 8 2 or 3 or 2 Glencoe/McGraw-Hill 97 Glencoe Pre-Algebra R eading to Learn Mathematics Pre-Activity How do negative exponents represent repeated division? Do the activity at the top of page 8 in your textbook. Write your answers below. a. Describe the pattern of powers in the first column. Continue the pattern by writing the next two powers in the table. The exponents decrease by ; 2 0,2. b. Describe the pattern of values in the second column. Then complete the second column. Each number is divided by 2;, 2. c. Verify that the powers you wrote in part a are equal to the values that you found in part b. See students work. d. Determine how 3 2 should be defined. 3 Reading the Lesson. Explain the value of 5 2 3 using a pattern. Sample answer: The value in each row is the previous value divided by 5, so 5 3 is 25. Power Value 5 5 5 0 5 2 5 5 2 2 2 5 5 2 3 25 2. Using what you know about the Quotient of Powers rule, fill in the missing number. 5 2 3? = 5 5 5 3 5 2 5 5 Helping You Remember 3. Are 2 x 2 and x 2 2 equivalent? Explain. Sample answer: No; let x = 3. 3 2 = 9, but 3 2 3 2 9. Glencoe/McGraw-Hill 98 Glencoe Pre-Algebra Glencoe/McGraw-Hill A8 Glencoe Pre-Algebra