In the following, simplify using absolute values as necessary. 4{m8}

Given information: An expression is given as ${\displaystyle \sqrt{4}\left\{m^8\right\}}$.
Calculations: We have been given an expression is ${\displaystyle \sqrt{4}\left\{m^8\right\}}$.
For finding the odd and even roots by using the absolute value as necessary, we must know about the power property of exponent i.e.
${\displaystyle {\left(a^m\right)}^n=a^{m\cdot n}}$.
${\displaystyle \Rightarrow \sqrt{4}\left\{m^8\right\}}$ [Simplify the fourth root of ${\displaystyle m^8}$]
${\displaystyle \Rightarrow \sqrt{4}\left\{{\left(m^2\right)}^4\right\}}$ [Break the power exponent in the form of ${\displaystyle {\left(a^m\right)}^n=a^{m\cdot n}}$]
${\displaystyle \Rightarrow \left|m^2\right|}$ [${\displaystyle \sqrt{n}\left\{a^n\right\}=\left|a\right|}$, if the value of n is even.]
Thus, index value of ${\displaystyle \sqrt{4}\left\{m^8\right\}}$ is even.
Hence, the simplification of ${\displaystyle \sqrt{4}\left\{m^8\right\}is\left|m^2\right|}$