Chapter 6.1, Problem 24OE

To determine

Whether the equation ${\left(\sqrt[5]{z}\right)}^5=z$ is true for all real values of $\left(z\right)$ .

Answer to Problem 24OE

Yes, the given equation is true.

Explanation of Solution

Given information: The given equation for variable $\left(z\right)$ which belongs to real is,

  ${\left(\sqrt[5]{z}\right)}^5=z\mathrm{......}\left(1\right)$

Calculation: From (1) ${\left(\sqrt[5]{z}\right)}^5=z$ is true for all $\left(z\right)$ belongs to real because of property,

  ${\left(\sqrt[n]{a}\right)}^n=a\text{ if }n\text{ is odd}$

Hence, the given equation is true for all $\left(z\right)$ belongs to real.