Check the solution to "In the following, simplify using absolute values signs..."

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Marenonigt

Answered question

2021-12-11

In the following, simplify using absolute values signs as needed.
$\sqrt[6]{128 b^{7}}$

Answer & Explanation

Philip Williams

Beginner2021-12-12Added 39 answers

Given information: An expression is given as $\sqrt[6]{128 b^{7}}$ .
Calculations: We have been given an expression is $\sqrt[6]{128 b^{7}}$ .
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, ${(a b)}^{m} = a^{m} \cdot b^{m}$ and the corresponding product property of radical expression is $\sqrt[n]{a b} = \sqrt[n]{a} * \sqrt[n]{b}$ .
$\Rightarrow \sqrt[6]{128 b^{7}}$ [Simplify the sixth root of $128 b^{7}$ with radical properties]
$\sqrt[6]{64 b * 2 b^{6}}$ [Rewrite $128 b^{7} = 64 b \cdot 2 b^{6}$ ]
$\Rightarrow \sqrt[6]{(2 b^{1})^{6}} * \sqrt[6]{2 b^{6}}$ [By using radical property $\sqrt[n]{a b} = \sqrt[n]{a} * \sqrt[n]{b}$ ]
$K \Rightarrow 2 | b | \sqrt[6]{2 b^{6}}$ [ $\sqrt[n]{a^{n}} = | a |$ , if the value of index is even]
Hence, the simplification of $\sqrt[6]{128 b^{7}} i s 2 | b | \sqrt[6]{2 b^{6}}$

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