Review: Exponents PDF - MTH 1W

U2 REVIEW: Exponents MTH 1W 1. Complete the table; Exponential Form Expanded Form Standard Form 2...

U2 REVIEW: Exponents MTH 1W 1. Complete the table; Exponential Form Expanded Form Standard Form 2 3 (− 3)(− 3)(− 3)(− 3) 5 2 16 625 2. Use exponent rules to express as a single power, then evaluate. 2 3 7 4 3 A. 3 ×3 B. (− 3) ÷ (− 3) C. 3 ( 2) 8 2 2 10 3 3 D. (− 4) (− 4)(− 4) E. 10 5 [ F. (− 2) ] 3. Simplify using exponent laws. 6 2 12 5 4 6 A. (𝑥 )(𝑥 ) B. 𝑑 ÷𝑑 C. (𝑚 ) 2 −3 4 𝑘 3 2 5 D. (𝑥 )(𝑥 )(𝑥) E. −3 F. (𝑏 ) (𝑏 ) 𝑘 4. Evaluate. 2 0 A. 5 0 B. (− 1) 0 C. ( ) 5 5. Use exponent rules to express with a single positive exponent, then evaluate. Final answer must be an integer or fraction. 5 7 3 −3 2 −4 0 A. 4 ÷ 4 [ B. (− 2) ] C. (3 )(3 )(3 ) 6. SImplify. Express your final answer with a positive exponent. 4 C. 𝑝 · ⎡⎢ 𝑝 −4 3 −2 −2 ⎤ A. (𝑥 )(𝑥 )(𝑥 ) B. 𝑚 𝑚 9 ⎣ ( ) ⎥ ⎦ 7. What exponent goes in the blank to make the following equation true? [ ] 6 𝑎 ×𝑎 12 2 =𝑎 𝑎 8. Simplify using exponent laws, then evaluate. 2 3 5 2 ×2 ×2 5 3 3 3 −1 A. 2 9 B. (− 3) 4 [ ] ÷ (− 3) 7 C. ( )( ) 4 4 9. Use exponent rules to express as a single power, then evaluate. Final answer must be an integer or fraction. −11 2 (−2) (−2) 3 −2 [(−2) ] 10. Complete the table. Standard Form Scientific Notation 24 900 000 5 1. 194 × 10 0. 000 000 000 541 −9 9. 05 × 10 11. A. Express the following in scientific notation. 2 Area of Canada 9 985 000 𝑘𝑚 2 Area of Poland 313 000 𝑘𝑚 Population of Canada 39 000 000 Population of Poland 40 600 000 B. Calculate the population density of Canada and Poland. How many times greater is the population density in Poland? 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 Population Density = 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑙𝑎𝑛𝑑 12. Evaluate. Write your answer in scientific notation. 3 9 (4. 5 × 10 )(7. 13 × 10 ) 13. Complete the table. Number Sets Example Natural Numbers Whole Numbers {..., − 2, − 1, 0, 1, 2,...} 3 1 4 , − 8. 25, 2 5 , 0. 3 Irrational Numbers 14. State the number of elements in each set. A. {2, 4, 6, 8, 10} B. {ham, turkey, salami} C. { } 15. List all of the subsets of {1, 2, 3}. 16. Identify the limit of each sequence. 5 5 5 5 A. 3. 1, 3. 01, 3. 001, 3. 0001,... B. 4. 3, 4. 33, 4. 333, 4. 3333,... C. 10, 5, 2 , 4 , 8 , 16 ,... 17. In the set of natural numbers from 1 to 100; A. What is the density of odd numbers? B. What is the density of single digit numbers? C. What is the density of numbers that contain a 4? 18. Which has a greater density; the set of real numbers between − 2 and 6 or the set of integers between − 2 and 6?  ANSWERS 1. 2 3 (3)(3) 9 4 (− 3) (− 3)(− 3)(− 3)(− 3) 81 5 2 (2)(2)(2)(2)(2) 32 2 4 ( ) 5 ( )( )( )( ) 2 5 2 5 2 5 2 5 16 625 5 3 6 5 3 9 2. A. 3 = 243 B. (− 3) =− 27 C. 3 = 729 D. (− 4) =− 1024 E. 10 = 1000 F. (− 2) =− 512 8 7 24 2 5 11 3. A. 𝑥 B. 𝑑 C. 𝑚 D. 𝑥 E. 𝑘 F. 𝑏 4. A. 1 B. 1 C. 1 1 1 1 −1 1 1 1 1 1 5. A. 2 = 16 B. 9 = 512 C. 2 = 9 6. A. 3 B. 8 C. 7 7. 8 4 (−2) 3 𝑥 𝑚 𝑝 3 2 8. A. 2 B. (− 3) 13 =− 1 594 323 C. ( ) 4 = 9 16 9. (−2) 1 3 = −1 8 10. 7 24 900 000 2. 49 × 10 5 119 400 1. 194 × 10 −10 0. 000 000 000 541 5. 41 × 10 −9 0. 000 000 009 05 9. 05 × 10 6 5 7 7 11. A. 9. 985 × 10 , 3. 13 × 10 , 3. 9 × 10 , 4. 06 × 10 B. Approximately 33 times greater 13 12. 3. 2085 × 10 13. Natural Numbers {1, 2, 3, 4, 5,...} Whole Numbers {0, 1, 2, 3, 4, 5...} Integers {..., − 2, − 1, 0, 1, 2,...} 3 1 Rational Numbers 4 , − 8. 25, 2 5 , 0. 3 Irrational Numbers π, 2 1 14. A. 5 B. 3 C. 0 15. { }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3} 16. A. 3 B. 4 3 or 4. 3 C. 0 1 9 19 17. A. 2 or 50% B. 100 or 9% C. 100 or 19% 18. The set of real numbers is more dense as there is an infinite number of real numbers, but only 7 integers between − 2 and 6.