simplify the radical
\sqrt[3]{125x^{6}y^{9}}
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We can simplify the radical \sqrt[3]{125x^{6}y^{9} by breaking down 125, x^{6}, and y^{9} into their prime factors:
125 = 5 * 5 * 5 = 5^3
x^6 = x * x * x * x * x * x = x^2 * x^2 * x^2 = (x^2)^3
y^9 = y * y * y * y * y * y * y * y * y = y^3 * y^3 * y^3 = (y^3)^3
Therefore,
\sqrt[3]{125x^{6}y^{9}} = \sqrt[3]{5^3 * (x^2)^3 * (y^3)^3}
= \sqrt[3]{5^3} * \sqrt[3]{(x^2)^3} * \sqrt[3]{(y^3)^3}
= 5x^2y^3
So, the simplified radical form is 5x^2y^3.