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Extra info for College Algebra Essentials
4x2 ≤ . 2 Exponents and Scientiﬁc Notation 27 SOLUTION 3 3 a. (-3x4 y5) = (-3)3(x4) (y5) # 3 # Raise each factor inside the parentheses to the third power. = (-3)3 x4 3 y5 3 Multiply the exponents when raising powers to powers. = -27x12 y15 (-3)3 = (-3)(- 3)(-3) = -27 b. (-7xy4)(-2x5 y6) = (-7)(-2)xx5 y4 y6 = 14x1 + 5 y4 + 6 When multiplying expressions with the same base, add the exponents. = 14x6 y10 c. -35x2 y4 5x6 y-8 = a = -7x-4 y12 = d. ¢ 4x2 ≤ y -3 = = = = = Simplify. y4 -35 x2 b ¢ 6 ≤ ¢ -8 ≤ 5 y x = -7x2 - 6 y4 - (-8) Group factors with the same base.
Woman, without her man, is nothing. Woman, without her, man is nothing. • What’s the latest dope? What’s the latest, dope? • Population of Amsterdam broken down by age and sex Population of Amsterdam, broken down by age and sex Name Meaning Examples Commutative Property of Addition Changing order when adding does not affect the sum. a + b = b + a • 13 + 7 = 7 + 13 • 13x + 7 = 7 + 13x Commutative Property of Multiplication Changing order when multiplying does not affect the product. • 12 # 15 = 15 # 12 • x # 6 = 6x ab = ba Associative Property of Addition Changing grouping when adding does not affect the sum.
7 Observe that -4 is to the left of -1 on the number line. This means that -4 is less than -1. −4 is less than −1 because −4 is to the left of −1 on the number line. 7, we can also observe that -1 is to the right of -4 on the number line. This means that -1 is greater than -4. –1>–4 −1 is greater than −4 because −1 is to the right of −4 on the number line. The symbols 6 and 7 are called inequality symbols. These symbols always point to the lesser of the two real numbers when the inequality statement is true.
College Algebra Essentials by Robert F. Blitzer