Section 1.6 Multiplication and Division of Real Numbers 59 Student Check 1 Multiply the real numbers. a. (-5)(3) b. (-12)(-2) c. 2 3 a- 3 2 b d. (-6)a- 1 18 b e. -5.71(100) f. (-7)(-3)(-4) g. (-8)(-9)(-2)a- 1 2 b ���������� Example 1(f) contains a product of three negative numbers and their product is negative. Example 1(g) contains a product of four negative numbers and their product is positive. The product of an even number of negative numbers is positive. The product of an odd number of negative numbers is negative. Simplifying Exponential Expressions In Section 1.3, we defined an exponent. Recall the following definition of an exponent. ������������������������ Exponents For b a real number and n a natural number, bn = b ∙ b ∙ b ∙ ∙ ∙ b n times where b is the base and n is the exponent. We will now examine what happens when a negative base is raised to an even or odd exponent. Negative Base Raised to an Even Exponent (2, 4, 6, . . .) Negative Base Raised to an Odd Exponent (1, 3, 5, . . .) (-5)2 = (-5)(-5) = 25 (-4)3 = (-4)(-4)(-4) = 16(-4) = -64 (-2)4 = (-2)(-2)(-2)(-2) = 4(-2)(-2) = -8(-2) = 16 (-3)5 = (-3)(-3)(-3)(-3)(-3) = 9(-3)(-3)(-3) = -27(-3)(-3) = (81)(-3) = -243 A negative base raised to an even exponent is positive. A negative base raised to an odd exponent is negative. Objective 2 ▶ Simplify exponential expressions.
hendricks_beginning_algebra_1e_ch1_3
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