58 Chapter 1 Whole Numbers Section 1.7 Exponents, Algebraic Expressions, 1. Exponents Thus far in the text we have learned to add, subtract, multiply, and divide whole numbers. We now present the concept of an exponent to represent repeated multiplication. For example, the product exponent 3 3 3 3 3 can be written as 35 base The expression is written in exponential form.The exponent, or power, is 5 and represents the number of times the base, 3, is used as a factor. The expression is read as “three to the fifth power.” Other expressions in exponential form are shown next. 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 54 55 is read as “five to the fifth power” 35 35 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 and the Order of Operations Concepts 1. Exponents 2. Square Roots 3. Order of Operations 4. Algebraic Expressions TIP: The expression 51 5. Any number without an exponent explicitly written has a power of 1. Skill Practice Evaluate. 1. 82 2. 43 3. 25
miller_prealgebra_2e_ch1_3
To see the actual publication please follow the link above