Question

ayuda
es para hoy
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Answer 1

Respuesta:

n = 5

Explicación paso a paso:

$\sqrt[3]{\frac{x^{ n-1}. \sqrt{x^{n} } }{\sqrt[6]{x^{5n-4} } } } = \sqrt[3]{\frac{x^{ n-1}. x^{\frac{n}{2} } }{{x^{\frac{5n-4}{6} } } } } = \sqrt[3]{\frac{ x^{\frac{2(n-1)+n}{2} } }{{x^{\frac{5n-4}{6} } } } }= \sqrt[3]{\frac{ x^{\frac{3n-2}{2} } }{{x^{\frac{5n-4}{6} } } } } = \sqrt[3]{x^{\frac{3n-2}{2}-{\frac{5n-4}{6} } } } = \sqrt[3]{x^{\frac{6(3n-2) -2(5n-4)}{(2)(6)} } } \\= \sqrt[3]{x^{\frac{18n - 12 -10n +8}{12} } } = \sqrt[3]{x^{\frac{8n-4}{12} } } ={x^{\frac{8n-4}{3(12)} } }$

$Como pide que se de primer grado , entonces la variable "x" debe estar elevada al exponente "1".\\{x^{\frac{8n-4}{3(12)} } }=x^{1} \\{\frac{8n-4}{3(12)} = 1$${\frac{8n-4}{36} = 1\\;8n - 4 = 36(1);\\\\8n - 4 = 36;\\8n = 36 + 4;\\\\8n = 40;\\\\n = \frac{40}{8}; \\n = 5$