Precalc0001to0005-page23

Precalc0001to0005-page23 - of x • If x ± x is the unique...

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(Section 0.5: Exponents and Radicals: Laws and Forms) 0.5.1 SECTION 0.5: EXPONENTS AND RADICALS: LAWS AND FORMS LEARNING OBJECTIVES • Be able to rewrite expressions in different forms. • Know laws of exponents and radicals and how to apply them. PART A: DISCUSSION • The mechanical manipulations in this section will prove useful in precalculus and calculus. Different forms of expressions are better suited to different processes. • We assume here that m and n are real numbers and that x and y take on real values. We only consider real -valued expressions for now. PART B: RADICALS is a radical symbol. In x n , n is the index , and x is the radicand . • We assume n is an integer such that n ± 2 . x , also written as x 1/ 2 , is the principal square root
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Unformatted text preview: of x . • If x ± , x is the unique nonnegative real number whose square is x . • The index here is 2. For example, 9 = 3 , and 9 1/2 = 3 . Although 9 has two square roots, 3 and ± 3 , we take the nonnegative square root as our principal square root . Also, = . We will discuss ± 1 in Section 2.1. x n , also written as x 1/ n , is the principal n th root of x . • If n is even and x ± , x n is the unique nonnegative real number whose n th power is x . • If n is odd , x n is the unique real number whose n th power is x . For example, 16 4 = 2 , and ± 8 3 = ± 2 . In Section 6.7, we will see that ± 8 has three complex cube roots, but only one is real ....
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