Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 0 - Section 0.2 - Exponents and Radicals - Exercises - Page 16: 78

Answer

$\displaystyle \frac{4}{3}x^{2}+\frac{1}{6}x^{3/2}- \displaystyle \frac{2}{3}x^{-2}$

Work Step by Step

Exponent form: An expression is in exponent form if * there are no radicals and * all powers of unknowns occur in the numerator. All terms in a sum or difference are of the form: (constant)(expression with x$)^{p}$ ----------------- First term: no adjustments, $\displaystyle \quad \frac{4}{3}x^{2}$ Second term: no adjustments, $\displaystyle \quad \frac{1}{6}x^{3/2}$ Third term: x is in the denominator, apply $a^{-n}=\displaystyle \frac{1}{a^{n}}=(\frac{1}{a})^{n}$ so it becomes$\quad \displaystyle \frac{2}{3}\cdot x^{-2}$ The expression, in exponent form is $\displaystyle \frac{4}{3}x^{2}+\frac{1}{6}x^{3/2}- \displaystyle \frac{2}{3}x^{-2}$
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