Translate all problems: To simplify the expression (\sqrt[4]{\frac{64x^9}{y^{12}}}), follow these steps: Simplify inside the radical: Break down the expression: (\sqrt[4]{64} \cdot \sqrt[4]{x^9} \cdot \sqrt[4]{\frac{1}{y^{12}}}). Simplify each part: (\sqrt[4]{64} = 2) because (64 = 2^6) and (\sqrt[4]{2^6} = 2^{6/4} = 2^{3/2} = 2\sqrt{2}). (\sqrt[4]{x^9} = x^{9/4}). (\sqrt[4]{\frac{1}{y^{12}}} = \frac{1}{y^{12/4}} = \frac{1}{y^3}). Combine the simplified parts: [ 2x^{9/4} \cdot \frac{1}{y^3} = 2x^{9/4}y^{-3} ] The simplified expression is: [ 2x^{9/4}y^{-3} ]