Section 1.7 Exponents, Square Roots, and the Order of Operations 63 is read as “five squared” or “five to the second power” is read as “five cubed” or “five to the third power” is read as “five to the fourth power” 52 53 55 is read as “five to the fifth power” Exponential form is a shortcut notation for repeated multiplication. However, to simplify an expression in exponential form, we often write out the individual factors. Evaluating Exponential Expressions Example 1 Evaluate. a. 62 b. 53 c. 24 Solution: a. The exponent, 2, indicates the number of times the base, 6, is used as a factor. 62 6 6 36 53 5 5 5 b. When three factors are multiplied, we can group the first two factors and perform the multiplication. Then multiply the product of the first two factors by the last factor. c. Group the first two factors. Multiply the first two factors. Multiply the product by the next factor to the right. 15 52 5 e e 1252 5 125 24 2 2 2 2 12 22 2 2 4 2 2 14 22 2 e 8 2 16 Answers 1. 64 2. 64 3. 32 One important application of exponents lies in recognizing powers of 10, that is, 10 raised to a whole-number power. For example, consider the following expressions. 101 10 102 10 10 100 103 10 10 10 1000 104 10 10 10 10 10,000 105 10 10 10 10 10 100,000 106 10 10 10 10 10 10 1,000,000 From these examples, we see that a power of 10 results in a 1 followed by several zeros. The number of zeros is the same as the exponent on the base of 10. Skill Practice Evaluate. 1. 82 2. 43 3. 25 TIP: The expression 51 5. Any number without an exponent explicitly written has a power of 1. 54
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