1. Section 1.6 Natural Number Exponents and Order of Operations

2. Objective 1: Use natural number exponents. 1.6 Natural Number Exponents and Order of Operations Repeated Multiplication: Exponential notation is a concise notation to indicate repeatedly multiplying the same factor a given number of times. The expression can be written using exponential notation. The base, or factor being repeatedly multiplied, is 2. The exponent, or number of times the factor is repeated, is 8. So Exponential notation is a concise notation to indicate repeatedly multiplying the same factor a given number of times..

3. Algebraically Verbally Numerical Examples For any natural number n, with base b and exponent n. For any natural number n, is the product of b used as a factor n times. The expression is read as “b to the nth power.” Exponential Notation

4. 1. 3. 2. 4. Write each expression in exponential form. Write each expression in expanded form.

5. To avoid errors it is very important to identify the base of an exponential expression. If an exponent is on a number or variable, then that number or variable is the base. If an exponent is outside a pair of grouping symbols, then the contents of this pair of grouping symbols is the base. Identify the correct base, exponent and expanded form of each expression. Exponential ExpressionBaseExponentExpanded Form 5. 6. 7. 8.

6. 9.10.11. Mentally evaluate each expression.

7. 12.13.14. Mentally evaluate each expression.

8. 16. and have the same value although the bases are different. Can you explain this? 15. Can you explain the subtle distinction between and ?

9. 17.(a) Which of the following do you think is the correct evaluation of the expression ? Option IOption IIOption III (b) Try evaluating the above expression on your calculator. Do you agree with the calculator result? Objective 2: Use the standard order of operations.

10. A major objective in this section is to master the order of operations. The order of operations gives a consistent method for evaluating mathematical expressions like the one above. Standard Order of Operations Step 1: Start with the expression within the innermost pair of ________________ ____________________. Step 2: Perform all __________________. Step 3: Perform all __________________ and __________________ as they appear from left to right. Step 4: Perform all __________________ and __________________ as they appear from left to right.

11. . The first four grouping symbols contain both a beginning symbol before and an ending symbol after the group. In the radical symbol and the fraction bar the group is determined by the length of the horizontal bar. Some common grouping symbols are

12. 18. 19.20. Use the standard order of operations to perform the indicated operations. Use a calculator only to check your results.

13. 21. 22.23. Use the standard order of operations to perform the indicated operations. Use a calculator only to check your results.

14. Use the standard order of operations to perform the indicated operations. Use a calculator only to check your results. 24. 25.

15. 26. 27. Use the standard order of operations to perform the indicated operations. Use a calculator only to check your results.

16. 28. 29. Use the standard order of operations to perform the indicated operations. Use a calculator only to check your results.

17. 30. 31. Use the standard order of operations to perform the indicated operations. Use a calculator only to check your results.

18. 32. 33. Use the standard order of operations to perform the indicated operations. Use a calculator only to check your results.

19. 34. 35. Use the standard order of operations to perform the indicated operations. Use a calculator only to check your results.

20. 36. 37. Use the standard order of operations to perform the indicated operations. Use a calculator only to check your results.

21. Objective 3: Use the distributive property of multiplication over addition. The distributive property can be used in two ways: to expand expressions that are in a factored form and to factor expressions with terms that have a common factor. Distributive Property of Multiplication Over Addition AlgebraicallyVerbally Numerical Examples For all real numbers a, b, and c, and. Multiplication distributes over addition.

22. Use the distributive property to expand each expression in the first column and to factor each expression in the second column. 38. 39.

23. Use the distributive property to expand each expression in the first column and to factor each expression in the second column. 40. 41.

24. 42. 43. Use the distributive property to expand each expression in the first column and to factor each expression in the second column.

25. 44. What property justifies the fact that ? 46. What property justifies the fact that ? 45. What property justifies the fact that ?

26. Adding Like Terms: Use the distributive property to combine like terms. 47. 48.

27. 49. 50. Adding Like Terms: Use the distributive property to combine like terms.

28. 51. 52. Adding Like Terms: Use the distributive property to combine like terms.

29. 53. 54. Adding Like Terms: Use the distributive property to combine like terms.

30. Phrases Used To Indicate Exponentiation Key PhrasesVerbal Examples Algebraic Examples To a power"3 to the 6 th power" Raised to "y raised to the 5 th power" Squared"4 squared" Cubed"x cubed"

31. 55. x raised to the fourth power 56. The square of the quantity x plus two. Translate each verbal statement into algebraic form.

32. 57.58. Write each expression in the horizontal one-line format used by calculators.

33. Each expression is given in the horizontal one-line format used by calculators. Rewrite each expression in the standard algebraic format. 59.60.