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hendricks_beginning_algebra_1e_ch1_3

28 Chapter 1 Real Numbers and Algebraic Expressions When the number n is a natural number, it indicates the number of times b is multiplied by itself or used as a factor. Some examples are illustrated next. Phrase Mathematical Expression 3 squared 32 = 3 · 3 = 9 5 cubed 53 = 5 · 5 · 5 = 125 6 to the 4th 64 = 6 · 6 · 6 · 6 = 1296 ���������������������� Evaluating an Exponential Expression Step 1: Identify the base and the exponent. Step 2: Rewrite the expression as repeated multiplication as indicated by the exponent. Step 3: Simplify the result. �� ������������������������ ������������������ Complete the chart by identifying the base, the exponent, and then evaluate the expression. Problems Base Exponent Evaluate 1a. 25 2 5 25 = 2 · 2 · 2 · 2 · 2 = 32 1b. 4.23 4.2 3 4.23 = (4.2)(4.2)(4.2) = 74.088 1c. a2 3 b 4 2 3 4 a2 3 b 4 = 2 3 · 2 3 · 2 3 · 2 3 = 16 81 1d. -62 6 2 We must find the opposite of 6 squared. -62 = - (6)(6) = -36 Student Check 1 Identify the base, the exponent, and then evaluate the expression. a. 103 b. 1.52 c. a6 7 b 3 d. -84 The Order of Operations The expression 5000(1.06)3, found in the section opener, is an example of an expression involving a combination of operations. This expression involves both multiplication and exponents. To simplify this expression, we need to know the order in which to perform the operations. Without an order to perform the operations, we would get different values for the same expression. If we multiply 5000 and 1.06 first in the expression 5000(1.06)3, we get 5000(1.06)3 = (5300)3 = 148,877,000,000 If we evaluate the exponential expression (1.06)3 first, we get 5000(1.06)3 = 5000(1.191016) = 5955.08 Sometimes expressions include grouping symbols such as parentheses ( ), brackets , braces { }, absolute value symbols u u, square roots 1 , or the fraction bar. Depending on where the grouping symbols are placed in an expression, different results may be obtained. To avoid confusion and errors, mathematicians developed an order for which we perform operations when simplifying expressions. This is called the order of operations and it is stated next. Objective 2 ▶ Use the order of operations to simplify numerical expressions.


hendricks_beginning_algebra_1e_ch1_3
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