Section 1.2 Exponents, Square Roots, and the Order of Operations 59 1. Exponential Expressions In algebra, repeated multiplication can be expressed using exponents.The expression can be written as exponent 43 base 43, 4 4 4 4 In the expression is the base, and 3 is the exponent, or power. The exponent indicates how many factors of the base to multiply. Concepts 1. Exponential Expressions 2. Square Roots 3. Order of Operations 4. Translations Definition of bn Let b represent any real number and n represent a positive integer. Then, bn b b b b p b ⎧⎪⎪⎪⎨⎪⎪⎪⎩ n factors of b is read as “b to the nth power.” bn b is called the base, and n is called the exponent, or power. b2 b3 is read as “b squared,” and is read as “b cubed.” The exponent, n, is the number of times the base, b, is used as a factor. Evaluating Exponential Expressions Example 1 Translate the expression into words and then evaluate the expression. a. b. c. d. Solution: a. The expression is read as “two to the fifth power.” 25 122122122122122 32 25 52 b. The expression is read as “five to the second power” or “five, squared.” 52 152152 25 c. The expression is read as “three-fourths to the third power” or “threefourths, cubed.” 16 a3 4b3 d. The expression is read as “one to the sixth power.” 16 112112112112112112 1 a3 4b a3 4b a3 4b 27 64 134 23 a 16 3 4b3 25 52 TIP: A number or variable with no exponent shown implies that there is an exponent of 1. That is, b b1. Skill Practice Evaluate. 1. 43 2. 24 2 3. a 4. 1127 Classroom Examples: p. 67, Exercises 26 and 28 Answers 1. 64 2. 16 3. 4. 1 4 9 3b2 Exponents, Square Roots, and the Order of Operations Section 1.2
miller_introductory_algebra_3e_ch1_3
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