Chapter 11 - Polynomial and Rational Functions - 11.1 Power Functions and Proportionality - Exercises and Problems for Section 11.1 - Exercises and Problems - Page 441: 41

$f(x)=\dfrac{-1}{3x \sqrt[3] 7}x^{-4/3}$

Power Function: $f(x)=nkx^{n-1} ~~~~(1)$ We are given that $F(x)=\dfrac{1}{\sqrt[3] 7}x^{-1/3}$ Plug $k=\dfrac{1}{\sqrt[3] 7}$and $n=\dfrac{-1}{3}$ in equation (1) to obtain: $f(x)=(\dfrac{-1}{3}) (\dfrac{1}{\sqrt[3] 7}) x^{-1/3-1}$ Thus, we can express the function as: $f(x)=\dfrac{-1}{3x \sqrt[3] 7}x^{-4/3}$