By Cynthia Y. Young

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Elementary-level textual content by way of famous Soviet mathematician bargains great advent to positive-integral parts of idea of persevered fractions. transparent, straight forward presentation of the homes of the equipment, the illustration of numbers via endured fractions and the degree thought of persevered fractions.

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90. Use your calculator to evaluate 91. Use your calculator to evaluate 14489. Does the answer appear to be a rational or an irrational number? Why? 882 . Does the answer A 49 appear to be a rational or an irrational number? Why? 92. 2 Page 18 I N T E G E R E X P O N E N TS A N D S C I E N T I F I C N O TAT I O N S K I LLS O BJ E CTIVE S ■ ■ ■ C O N C E P TUAL O BJ E CTIVE S ■ Evaluate expressions involving integer exponents. Apply properties of exponents. Use scientiﬁc notation. ■ Visualize negative exponents as reciprocals.

27x3 y9 z6 c. qxd 22 8/7/12 5:34 PM Page 22 C H A P T E R 0 Prerequisites and Review Simplifying Exponential Expressions EXAMPLE 6 Write each expression so that all exponents are positive (assume all variables are nonzero). (x2 y-3) 2 a. (3x2 z-4) -3 b. -1 4 -3 (x y ) 3 c. (-2xy2) 3 2 -(6xz ) Solution (a): Apply the product to a power property. (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.

1 Real Numbers 11 Using the Distributive Property EXAMPLE 7 Use the distributive property to eliminate the parentheses. a. 3(x ϩ 5) b. 2(y Ϫ 6) Solution (a): ➤ 3(x ϩ 5) ϭ 3(x) ϩ 3(5) Use the distributive property. ϭ 3x ϩ 15 Perform the multiplication. Solution (b): ➤ 2(y Ϫ 6) ϭ 2(y) Ϫ 2(6) Use the distributive property. ϭ 2y Ϫ 12 Perform the multiplication. ■ YO U R T U R N ■ Use the distributive property to eliminate the parentheses. a. 2(x ϩ 3) Answer: a. 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.