Question

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

Answer 1

`\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}`