Question

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

Answer 1

Answer:

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

Step-by-step explanation:

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

$\sqrt[3]{\frac{10x^{5} }{54x^{8} } }$

Let's first simplify the x's:

$\sqrt[3]{\frac{10}{54x^{3} } }$

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

$\sqrt[3]{\frac{10}{2 * 27x^{3} } } = \sqrt[3]{\frac{5}{27x^{3} } }$

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

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