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What is the simplest radical form of the expression?

 

(x4y7)2/3

 Feb 28, 2018
 #1
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\(\quad(x^4y^7)^{\frac23}\\ =\\ \quad(x^4)^{\frac23}(y^7)^{\frac23}\\ =\\ \quad x^{4\cdot\frac23}y^{7\cdot\frac23}\\ =\\ \quad x^\frac83y^\frac{14}3 \\ =\\ \quad x^\frac63x^\frac23y^\frac{12}3y^\frac23\\ =\\ \quad x^2x^\frac23y^4y^\frac23 \\ =\\ \quad x^2y^4(xy)^\frac23\\ =\\ \quad x^2y^4\sqrt[3]{(xy)^2} \\ =\\ \quad x^2y^4\sqrt[3]{x^2y^2}\)

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 Feb 28, 2018

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