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**Sample text**

We obtain the same distance if we reverse the order of the subtraction: ͉ 3 - (-5) ͉ = ͉ 8͉ = 8. ● ● ● Check Point 7 Find the distance between -4 and 5 on the real number line. ᕩ Identify properties of the real numbers. Properties of Real Numbers and Algebraic Expressions When you use your calculator to add two real numbers, you can enter them in any order. The fact that two real numbers can be added in any order is called the commutative property of addition. 2, without giving it much thought.

Just as the commutative properties change groupings, the associative properties change order. In Exercises 148–155, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 148. 149. 150. 151. 152. 153. 154. 155. Every rational number is an integer. Some whole numbers are not integers. Some rational numbers are not positive. Irrational numbers cannot be negative. The term x has no coefﬁcient. 2 Objectives ᕡ Use the product rule.

32,000 78. 64,000 79. 638,000,000,000,000,000 80. 579,000,000,000,000,000 23 21. 7 2 34 22. 7 3 81. -5716 82. - 3829 83. 0027 84. 0083 85. 00000000504 86. 00000000405 Simplify each exponential expression in Exercises 23–64. 23. x-2 y 24. xy-3 25. x0 y5 26. x7 y0 29. x-5 # x10 30. x-6 # x12 27. x3 # x7 28. x11 # x5 3 7 11 5 31. (x ) 33. (x-5) In Exercises 87–106, perform the indicated computations. Write the answers in scientiﬁc notation. If necessary, round the decimal factor in your scientiﬁc notation answer to two decimal places.