Get the solution to "In the following, simplify using absolute values as..."

Sapewa

Answered question

2021-12-06

In the following, simplify using absolute values as necessary.

\sqrt{4} {m^{8}}

Heather Fulton

Beginner2021-12-07Added 31 answers

Given information: An expression is given as

\sqrt{4} {m^{8}}

.
Calculations: We have been given an expression is

\sqrt{4} {m^{8}}

.
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.

{(a^{m})}^{n} = a^{m \cdot n}

\Rightarrow \sqrt{4} {m^{8}}

[Simplify the fourth root of

m^{8}

]

\Rightarrow \sqrt{4} {{(m^{2})}^{4}}

[Break the power exponent in the form of

{(a^{m})}^{n} = a^{m \cdot n}

]

\Rightarrow | m^{2} |

[

\sqrt{n} {a^{n}} = | a |

, if the value of n is even.]
Thus, index value of

\sqrt{4} {m^{8}}

is even.
Hence, the simplification of

\sqrt{4} {m^{8}} i s | m^{2} |

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