29 R.3 Real Number Operations and Properties Read an as “a to the nth power” or simply “a to the nth.” Exponential Notation If n is any positive integer and a is any real number, then the nth power of a is written using exponential notation as follows. an =a # a # a # N# a e n factors of a Order of Operations If grouping symbols such as parentheses, square brackets, absolute value bars, or fraction bars are present, begin as follows. Step 1 Work separately above and below each fraction bar. Step 2 Use the rules below within each set of parentheses or square brackets. Start with the innermost set and work outward. If no grouping symbols are present, follow these steps. Step 1 Simplify all powers and roots. Work from left to right. Step 2 Do any multiplications or divisions in order. Work from left to right. Step 3 Do any negations, additions, or subtractions in order. Work from left to right. EXAMPLE 4 Evaluating Exponential Expressions Evaluate each exponential expression, and identify the base and the exponent. (a) 43 (b) 1-622 (c) -62 (d) 4 # 32 (e) 14 # 322 SOLUTION (a) 43 = 4 # 4 # 4 = 64 The base is 4 and the exponent is 3. • 3 factors of 4 (b) 1-622 = 1-621-62 = 36 The base is -6 and the exponent is 2. (c) -62 = -16 # 62 = -36 The base is 6 and the exponent is 2. (d) 4 # 32 = 4 # 3 # 3 = 36 The base is 3 and the exponent is 2. (e) 14 # 322 = 122 = 144 The base is 4 # 3, or 12, and the exponent is 2. S Now Try Exercises 81, 83, and 87. Notice that parts (b) and (c) are different. 32 = 3 # 3, NOT 3 # 2 14 # 322 ≠4 # 32 Order of Operations When an expression involves more than one operation symbol, such as 5 # 2 + 3, we use the following order of operations.
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