Sapewa

2021-12-06

In the following, simplify using absolute values as necessary.

$\sqrt{4}\left\{{m}^{8}\right\}$

Heather Fulton

Beginner2021-12-07Added 31 answers

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.

$\left({a}^{m}\right)}^{n}={a}^{m\cdot n$ .

$\Rightarrow \sqrt{4}\left\{{m}^{8}\right\}$ [Simplify the fourth root of $m}^{8$ ]

$\Rightarrow \sqrt{4}\left\{{\left({m}^{2}\right)}^{4}\right\}$ [Break the power exponent in the form of $\left({a}^{m}\right)}^{n}={a}^{m\cdot n$ ]

$\Rightarrow \left|{m}^{2}\right|$ [$\sqrt{n}\left\{{a}^{n}\right\}=\left|a\right|$ , if the value of n is even.]

Thus, index value of$\sqrt{4}\left\{{m}^{8}\right\}$ is even.

Hence, the simplification of$\sqrt{4}\left\{{m}^{8}\right\}\text{}is\text{}\left|{m}^{2}\right|$

Calculations: We have been given an expression is

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.

Thus, index value of

Hence, the simplification of