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Which expression is equivalent to...? Assume... screenshots attached, please help!

Which expression is equivalent to...? Assume... screenshots attached, please help-example-1

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Answer:


\frac{\sqrt[3]{5} }{3x}

Explanation:

Ok, let's do this step by step....


\sqrt[3]{(10x^(5) )/(54x^(8) ) }

Let's first simplify the x's:


\sqrt[3]{(10)/(54x^(3) ) }

Then we breakdown the 54 as 2 * 27 then simplify with the 10 above.


\sqrt[3]{(10)/(2 * 27x^(3) ) } = \sqrt[3]{(5)/(27x^(3) ) }

Now, we can rewrite this as the following and solve the bottom part:


\frac{\sqrt[3]{5} }{\sqrt[3]{27x^(3) } } = \frac{\sqrt[3]{5} }{3 \sqrt[3]{x^(3) } } = \frac{\sqrt[3]{5} }{3x}

The solution is


\frac{\sqrt[3]{5} }{3x}

User Ruchir Shukla
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