By Cynthia Y. Young
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Additional resources for Algebra & Trigonometry
3x2 z-4) -3 -3 -3 = (3) (x2) (z-4) Apply the power property. ϭ 3Ϫ3 xϪ6 z12 Apply the negative-integer exponent property. = Evaluate 33. = -3 z12 33 x6 z12 27x6 Solution (b): (x2 y-3) 2 Apply the product to a power property. (x-1 y4) -3 = x4 y-6 x3 y-12 Apply the quotient property. ϭ x4Ϫ3 yϪ6Ϫ(Ϫ12) Simplify. ϭ xy6 Solution (c): Apply the product to a power property on both the numerator and denominator. ■ Answer: 2t v3 (-2xy2)3 3 2 -(6xz ) = (- 2)3(x)3(y2)3 2 -(6)2(x)2(z3) -8x3 y6 Apply the power property.
A a = b b a a = -b b - 16 = -4 4 15 = -5 -3 A negative quantity times a negative quantity is a positive quantity. (Ϫa)(Ϫb) ϭ ab (Ϫ2x)(Ϫ5) ϭ 10x A negative quantity divided by a negative quantity is a positive quantity. -a a = -b b - 12 = 4 -3 The opposite of a negative quantity is a positive quantity (subtracting a negative quantity is equivalent to adding a positive quantity). Ϫ(Ϫa) ϭ a Ϫ(Ϫ9) ϭ 9 A negative sign preceding an expression is distributed throughout the expression. Ϫ(a ϩ b) ϭ Ϫa Ϫ b Ϫ(a Ϫ b) ϭ Ϫa ϩ b Ϫ3(x ϩ 5) ϭ Ϫ3x Ϫ 15 Ϫ3(x Ϫ 5) ϭ Ϫ3x ϩ 15 EXAMPLE 8 or or Using Properties of Negatives Eliminate the parentheses and perform the operations.
2x ϩ 6 b. 5y Ϫ 15 b. 5(y Ϫ 3) You also probably know the rules that apply when multiplying a negative real number. ” P R O P E RTI E S O F N E GATIVE S MATH (LET a DESCRIPTION AND b BE POSITIVE REAL NUMBERS) EXAMPLE A negative quantity times a positive quantity is a negative quantity. (Ϫa)(b) ϭ Ϫab (Ϫ8)(3) ϭ Ϫ24 A negative quantity divided by a positive quantity is a negative quantity. or A positive quantity divided by a negative quantity is a negative quantity. -a a = b b a a = -b b - 16 = -4 4 15 = -5 -3 A negative quantity times a negative quantity is a positive quantity.
Algebra & Trigonometry by Cynthia Y. Young