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

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berljivx8

Answered question

2021-12-10

In the following, simplify using absolute values as necessary.
$\sqrt[5]{32 b^{20}}$

Answer & Explanation

lenkiklisg7

Beginner2021-12-11Added 29 answers

Given information: An expression is given as $\sqrt[5]{32 b^{20}}$ .
Calculations: We have been given an expression is $\sqrt[5]{32 b^{20}}$ .
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.
${(a^{m})}^{n} = a^{m \cdot n}$
$\sqrt[5]{32 b^{20}}$ [Simplify the cube root of $32 b^{20}$ ]
$\Rightarrow \sqrt[5]{(2 b^{4})^{5}}$ [Break the power exponent in the form of ${(a^{m})}^{n} = a^{m \cdot n}$ ]
$\Rightarrow 2 b^{4}$ [ $\sqrt[n]{a^{n}} = a$ , if the value of n is odd.]
Thus, index value of $\sqrt[5]{32 b^{20}}$ is odd.
Hence, the simplification of $\sqrt[5]{32 b^{20}} i s 2 b^{4}$

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