Stitz-Zeager_College_Algebra_e-book

The rst base 10 is often called the common base the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The proof of Theorem 5.6 is based on the definition of the principal roots and properties of expo√ nents. To establish the product rule, consider the following. If n is odd, then by definition n xy √√n √n√n √n is the unique real number such that ( n xy ) = xy . Given that n x n y = ( n x) n y = xy , √√ √ √ it must be the case that n xy = n x n y . If n is even, then n xy is the unique non-negative real √ √n √ number such that ( n xy ) = xy . Also note that since n is even, n x and n y are also non-negative √√ √√ √ and hence so is n x n y . Proceeding as above, we find that n xy = n x n y . The quotient rule is proved similarly and is left as an exercise. The power rule results from repeated application of the √ product rule, so long as n x is a real number to start with.2 The last property is an application of the power rule when n is odd, and the occurrence of the absolute value √ when n is even is due to √ 4 n 4 = 4 16 = 2 = | − 2|, not −2. the requirement that x ≥ 0 in Definition 5.4. For instance, (−2) It’s this la...
View Full Document

Ask a homework question - tutors are online