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hunterofdeath63

Answered question

2021-12-09

In the following, simplify using absolute values as necessary.
$\sqrt[3]{8 a^{51} b^{6}}$

Answer & Explanation

Jeffery Autrey

Beginner2021-12-10Added 35 answers

Given information: An expression is given as $\sqrt[3]{8 a^{51} b^{6}}$ .
Calculations: We have been given an expression is $\sqrt[3]{8 a^{51} b^{6}}$ .
To simplify the odd and even roots by using the absolute value as necessary, we will use power property of exponent i.e. ${(a^{m})}^{n} = a^{m \cdot n}$ as shown below:
$\Rightarrow \sqrt[3]{8 a^{51} b^{6}}$ [Simplify the square root of $8 a^{51} b^{6}$ ]
$\Rightarrow \sqrt[3]{(2 a^{17} b^{2})^{3}}$ [Break the power exponent in the form of ${(a^{m})}^{n} = a^{m \cdot n}$ ]
$\Rightarrow 2 a^{17} b^{2}$ [ $\sqrt[n]{a^{n}} = | a |$ , if the value of n is odd.]
Thus, index of $\sqrt[3]{8 a^{51} b^{6}}$ is odd.
Hence, the simplification $\sqrt[3]{8 a^{51} b^{6}} i s 2 a^{17} b^{2}$

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