simplify

Is your question supposed to be formatted like this?: (250x^6)^3

\(\sqrt[3]{250x^6}\)

So, in this case, a cube root is the same as that value to the power of 1/3.

\((250x^6)^{\frac{1}{3}}\)

Then, you just multiply the exponents by each other. 

\(6*\frac{1}{3}=\frac{6}{3}=2\)

So that makes it:

\(250x^2\)

simplify

\(\mathbf{\large{\sqrt[3]{250x^6}}}\)

\(\begin{array}{|rcll|} \hline && \mathbf{\large{\sqrt[3]{250x^6}}} \\ &=& \sqrt[3]{250}\sqrt[3]{x^6} \\ &=& \sqrt[3]{250}\cdot x^{\frac{6}{3}} \\ &=& \sqrt[3]{250}\cdot x^{2} \\ &=& \sqrt[3]{2\cdot125}\cdot x^{2} \\ &=& \sqrt[3]{2}\sqrt[3]{125}\cdot x^{2} \\ &=& \sqrt[3]{2}\sqrt[3]{5^3}\cdot x^{2} \\ &=& \sqrt[3]{2}\cdot 5^{\frac{3}{3}} \cdot x^{2} \\ &=& \sqrt[3]{2}\cdot 5^{1} \cdot x^{2} \\ &\mathbf{=}& \mathbf{\sqrt[3]{2}\cdot 5 \cdot x^{2} } \\ \hline \end{array}\)