College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.2 - Exponential Functions - 4.2 Exercises - Page 409: 10

Answer

$\frac{\sqrt{3}}{27}$

Work Step by Step

Substitute $\frac{-5}{2}$ to x. $f(\frac{-5}{2})$ $=3^{\frac{-5}{2}}$ Use the rule $a^{-b}=\frac{1}{a^b}, b\gt0$. $=\frac{1}{3^{\frac{5}{2}}}$ $=\frac{1\times3^{\frac{1}{2}}}{3^{\frac{5}{2}}\times3^{\frac{1}{2}}}$ Rationalize the denominator by multiplying $3^{\frac{1}{2}}$ to the numerator and denominator. $=\frac{3^{\frac{1}{2}}}{3^{\frac{6}{2}}}$ Simplify. $=\frac{3^{\frac{1}{2}}}{3^3}$ $=\frac{\sqrt{3}}{27}$
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