Chapter 13.7, Problem 10MRE

To determine

To simplify: The given function.

Answer to Problem 10MRE

The simplification of the given function is $x$ .

Explanation of Solution

Given:

The given function is,

  ${\left(\frac{x^{2/3}}{x^{1/2}}\right)}^6$

Calculation:

Solve the given function,

  $\begin{array}{c}{\left(\frac{x^{2/3}}{x^{1/2}}\right)}^6=\frac{x^{2\left(\frac{6}{3}\right)}}{x^{1\left(\frac{6}{2}\right)}}\\ =\frac{x^4}{x^3}\\ =x^{4-3}\\ =x\end{array}$

Thus, the simplification of the given function is $x$ .