Algebra & Trigonometry by Cynthia Y. Young

By Cynthia Y. Young

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Rewrite the number with the implied decimal point. ■ Answer: a. 52 ϫ 109 b. 3 ϫ 10Ϫ7 Move the decimal point to the left 15 places. 856 ϫ 1015 b. Move the decimal point to the right 6 places. 75 ϫ 10Ϫ6 ■ YO U R T U R N Express the numbers in scientific notation. a. 4,520,000,000 EXAMPLE 8 Technology Tip 3,856,000,000,000,000. b. 00000043 Converting from Scientific Notation to Decimals Write each number as a decimal. a. 869 ϫ 105 b. 03 ϫ 10Ϫ3 Solution: a. Move the decimal point 5 places to the right (add zeros in between).

Qxd 8/7/12 5:34 PM Page 3 I N T H I S C H A P T E R real numbers, integer exponents, and scientific notation will be discussed, followed by rational exponents and radicals. Simplification of radicals and rationalization of denominators will be reviewed. Basic operations such as addition, subtraction, and multiplication of polynomials will be discussed followed by a review of how to factor polynomials. Rational expressions will be discussed and a brief overview of solving simple algebraic equations will be given.

4xy7 Answer: a. Ϫ12x4 y5 b. Ϫ27x3 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.

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