Section 1.3 Exponents, Square Roots, and the Order of Operations 35 Exponents, Square Roots, and the Order of Operations 43, 4 43 In the expression is the base, and 3 is the exponent, or power. The exponent indicates how many factors of the base to multiply. Definition of bn Let b represent any real number and n represent a positive integer.Then, bn b b b b . . . 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. 3 4 3 a. b. c. d. Solution: a. The expression 25 is read as “two to the fifth power.” 25 122122122122122 32 52 b. The expression is read as “five to the second power” or “five, squared.” c. The expression is read as “three-fourths to the third power” or “threefourths, cubed.” 16 a 3 4 3 a d. The expression is read as “one to the sixth power.” Skill Practice Evaluate. 1. 43 2. 24 3. a 4. 1127 2 3 2 b 16 112112112112112112 1 b 3 4 b a 3 4 b a 3 4 b 27 64 134 23 52 152152 25 a b 16 25 52 Section 1.3 TIP: A number or variable with no exponent shown implies that there is an exponent of 1. That is, b b1. Answers 1. 64 2. 16 3. 4. 1 4 9 1. Exponential Expressions In algebra, repeated multiplication can be expressed using exponents.The expression can be written as exponent base 4 4 4 Concepts 1. Exponential Expressions 2. Square Roots 3. Order of Operations 4. Translations
miller_beginning_intermediate_algebra_4e_ch1_3
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