Chapter 6.4, Problem 59HP

To determine

Whether the expression $\sqrt[4]{16x^4{y}^8}$ simplified by Ashley and Kimi are correct or not.

Answer to Problem 59HP

The expression $\sqrt[4]{16x^4{y}^8}$ simplified by Kimi is correct.

Explanation of Solution

Given information: The expressions simplified by Ashley and Kimi are written as,

  $\begin{array}{l}\left(\begin{array}{c}\sqrt[4]{16x^4{y}^8}=\sqrt[4]{{\left(2x{y}^2\right)}^4}\\ =2\left|x{y}^2\right|\end{array}\right)\mathrm{......}\left(\text{Ashley}\right)\\ \left(\begin{array}{c}\sqrt[4]{16x^4{y}^8}=\sqrt[4]{{\left(2x{y}^2\right)}^4}\\ =2y^2\left|x\right|\end{array}\right)\mathrm{......}\left(\text{Kimi}\right)\end{array}$

Calculation: From the expression written by Ashley and Kimi, the expression written by Kimi is correct because the expression simplified by Kimi has absolute sign on $\left(x\right)$ because $\sqrt[4]{16x^4{y}^8}$ is even root function and after simplification even power of $\left(x^4\right)$ changes to odd power of $\left(x\right)$ . Hence, absolute sign must be on $\left(x\right)$ , whereas in case of Ashley absolute sign is also put on $\left(y^2\right)$ which is not required.

Hence, the expression simplified by Kimi is correct.