<s>[INST] How to simplify $\frac{\sqrt{x^3}}{\sqrt[3]{x^4}}$? Please, could someone help simplify and show the steps on how to simplify $$\frac{\sqrt{x^3}}{\sqrt[3]{x^4}}?$$
Thank you.
 [/INST] $$\large{\sqrt{x^3} = (x^3)^{\frac{1}{2}} = x^{\frac{3}{2}}}$$
Now 
$$\large{\sqrt[3]{x^4} = (x^4)^{\frac{1}{3}} = x^{\frac{4}{3}}}$$
Now you divide these two $$\large{\frac{x^{\frac{3}{2}}}{x^{\frac{4}{3}}} = x^{\frac{3}{2}-\frac{4}{3}} = \color{red}{x^{\frac{1}{6}} =\sqrt[6]{x}}}$$
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