Question

Raiz cúbica de 2 sobre raiz quinta de 4 é igual à?

Answer 1

$\cfrac{\sqrt[3]{2} }{\sqrt[5]{4} } \\\\\\= \cfrac{\sqrt[15]{2^5} }{\sqrt[15]{4^3} } \\\\\\= \cfrac{\sqrt[15]{4^2 \cdot 2} }{\sqrt[15]{4^2 \cdot 2 \cdot 2} }\\\\\\= \cfrac{\sqrt[15]{4^2 \cdot 2} }{\sqrt[15]{4^2 \cdot 2} \cdot \sqrt[15]{2} }\\\\\\= \cfrac{1}{\sqrt[15]{2} } \\\\= (\sqrt[15]{2} )^{-1}\\\\= (2^{\frac{1}{15} })^{-1}\\\\= 2^{\frac{1}{15} \cdot (-1) }\\\\= \boxed{\boxed{2^{-\frac{1}{15} }}}$