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04-03-2019
Mathematics

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simplify the radical expression

^3sqrt 125x^9 y^12

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jdoe0001 jdoe0001

04-03-2019

[tex]\bf \sqrt[3]{125x^9y^{12}}~~ \begin{cases} 125=5\cdot 5\cdot 5\\ \qquad 5^3\\ x^9=x^{3\cdot 3}\\ \qquad (x^3)^3\\ y^{12}=y^{4\cdot 3}\\ \qquad (y^4)^3 \end{cases}\implies \sqrt[3]{5^3(x^3)^3(y^4)^3}\implies 5x^3y^4[/tex]

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