In the following, simplify using absolute values signs as needed. \sqrt[5]{96a^{7}}

jamessinatraaa

jamessinatraaa

Answered question

2021-12-06

In the following, simplify using absolute values signs as needed.
5{96a7}

Answer & Explanation

Melissa Moore

Melissa Moore

Beginner2021-12-07Added 32 answers

Given information: An expression is given as 5{96a7}.
Calculations: We have been given an expression is 5{96a7}.
To simplify the radical expressions by using absolute value as needed, we must know about the radical properties and the index value of root is even or odd as shown below:
We know that, (ab)m=ambm and the corresponding product property of radical expression is n{ab}=n{a}n{b}.
5{96a7} [Simplify the fifth root of \sqrt[5]{96a^{7}} with radical properties]
5{32a3a2} [Rewrite 96a7=32a3a2]
5{(2a)5}5{3a2} [By using radical property n{ab}=n{a}n{b}]
2a5{3a2} [n{an}=|a|, if the value of index is odd]
\Rightarrow 2a\sqrt[5]{3a^{2}}
Hence, the simplification of 5{96a7} is 2a5{3a2}

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