Sapewa

2021-12-06

In the following, simplify using absolute values as necessary.
$\sqrt{4}\left\{{m}^{8}\right\}$

Heather Fulton

Given information: An expression is given as $\sqrt{4}\left\{{m}^{8}\right\}$.
Calculations: We have been given an expression is $\sqrt{4}\left\{{m}^{8}\right\}$.
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.
${\left({a}^{m}\right)}^{n}={a}^{m\cdot n}$.
$⇒\sqrt{4}\left\{{m}^{8}\right\}$ [Simplify the fourth root of ${m}^{8}$]
$⇒\sqrt{4}\left\{{\left({m}^{2}\right)}^{4}\right\}$ [Break the power exponent in the form of ${\left({a}^{m}\right)}^{n}={a}^{m\cdot n}$]
$⇒|{m}^{2}|$ [$\sqrt{n}\left\{{a}^{n}\right\}=|a|$, if the value of n is even.]
Thus, index value of $\sqrt{4}\left\{{m}^{8}\right\}$ is even.
Hence, the simplification of

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