I am suppose to simplify. (Write the result with as small an index as possible.) Assuming that each variable is nonnegative. How do I go about writing out the steps to solving this problem?
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$\displaystyle ^6\sqrt{27} = 27^{\frac{1}{6}}$ $\displaystyle 27^{\frac{1}{6}} = {3^3}^{\frac{1}{6}}$ $\displaystyle {3^3}^{\frac{1}{6}} = 3^{\frac{3}{6}}$ $\displaystyle 3^{\frac{3}{6}} = 3^{\frac{1}{2}}$ $\displaystyle 3^{\frac{1}{2}} = \sqrt{3}$
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