<s>[INST] Simplify $\sqrt[3]{162x^6y^7}$ The answer is $3x^2 y^2 \sqrt[3]{6y}$
How does $\sqrt[3]{162x^6y^7}$ equal $3x^2 y^2\sqrt[3]{6y}$?
 [/INST] First note that 162 factors as $2\cdot 3^4$. So collecting our powers of 3 reveals
$$\sqrt[3]{162x^6y^7}  = \sqrt[3]{3^3 \cdot (x^3)^2\cdot (y^3)^2 \cdot (2\cdot 3  \cdot y)}  = 3x^2y^2\sqrt[3]{6y}.$$
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