Chapter 11 - Polynomial and Rational Functions - 11.1 Power Functions and Proportionality - Exercises and Problems for Section 11.1 - Exercises and Problems - Page 441: 42

$f(x)=\dfrac{5}{28}x^{7/5}$

Here, $f(x)=\dfrac{kx^{n+1}}{n+1} ~~~~(1)$ We are given that $f(x)=\dfrac{\sqrt[5] {x^2}}{4}$ Plug $k=\dfrac{1}{4}$and $n=\dfrac{2}{5}$ in equation (1) to obtain: $f(x)=\dfrac{\dfrac{1}{4}x^{2/5+1}}{\dfrac{2}{5}+1}$ Thus, we can express the function as: $f(x)=\dfrac{5}{28}x^{7/5}$