By Cynthia Y. Young

ISBN-10: 0470648031

ISBN-13: 9780470648032

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The properties of integer exponents require the same base. We will now use properties of integer exponents to simplify exponential expressions. An exponential expression is simpliﬁed when: ■ ■ ■ ■ All parentheses (groupings) have been eliminated. A base appears only once. No powers are raised to other powers. All exponents are positive. EXAMPLE 5 Simplifying Exponential Expressions Simplify the expressions (assume all variables are nonzero). 3 a. (- 2x2 y3)(5x3 y) b. (2x2 yz3) c. 25x3 y6 -5x5 y4 Solution (a): Parentheses imply multiplication.

21 ϩ 2 Perform the addition. ϭ 23 ■ YO U R T U R N Evaluate the algebraic expression 6y ϩ 4 for y ϭ 2. In Example 6, the value for the variable was speciﬁed in order for us to evaluate the algebraic expression. What if the value of the variable is not speciﬁed; can we simplify an expression like 3(2x Ϫ 5y)? In this case, we cannot subtract 5y from 2x. Instead, we rely on the basic properties of real numbers, or the basic rules of algebra. Properties of Real Numbers You probably already know many properties of real numbers.

4, Ϫ3, Ϫ2, Ϫ1, 0, 1, 2, 3, . }, which is a subset of the set of rational numbers, which is a subset of the set of real numbers. The three dots, called an ellipsis, indicate that the pattern continues indeﬁnitely. If a set has no elements, it is called the empty set, or null set, and is denoted by the symbol л. The set of real numbers consists of two main subsets: rational and irrational numbers. Rational Number DEFINITION A rational number is a number that can be expressed as a quotient (ratio) of two a integers, , where the integer a is called the numerator and the integer b is called the b denominator and where b Z 0.

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