Question

Simplificando a expressão √((x^3/2)/(∛x⁴)), obtém-se:
A) ¹²√x
B) ⁶√x⁵
C) ¹²√x⁵
D) ⁶√x

Answer 1

Resposta:

A

Explicação passo a passo:

$\sqrt{\frac{x^{\frac{3}{2} } }{\sqrt[3]{x^{4} } } } \\\\\sqrt{\frac{x^{\frac{3}{2} } }{x^{\frac{4}{3} } } } } } \\\\Simplifique: \\x^{\frac{3}{2}-\frac{4}{3} } \\\\x^{\frac{1}{6} } \\\\Voltando a raiz:\\\sqrt{x^{\frac{1}{6} } } \\\\(x^{\frac{1}{6} })^{\frac{1}{2} } \\\\Simplifique:\\x^{\frac{1}{6}.\frac{1}{2} } \\\\x^{\frac{1}{12} } \\Transforma de volta numa raiz:\\\\\sqrt[12]{x}$