Question

raiz Quinta de 2^x * raiz cúbica de 4^x = raiz quadrada de 8^-x

Answer 1

$\sqrt[5]{2^x}.\sqrt[3]{4^x}=\sqrt{8^{-x}}\ \to\ \sqrt[5]{2^x}.\sqrt[3]{(2^2)^x}=\sqrt{(2^3)^{-x}}\\\\ (2^x)^{\frac{1}{5}}.(2^{2x})^{\frac{1}{3}}=(2^{-3x})^{\frac{1}{2}}\ \to\ 2^{\frac{x}{5}}.2^{\frac{2x}{3}}=2^{\frac{-3x}{2}}\\\\ 2^{\frac{x}{5}+\frac{2x}{3}}=2^{\frac{-3x}{2}}\ \to\ 2^{\frac{3x+10x}{15}}=2^{\frac{-3x}{2}}\\\\ 2^{\frac{13x}{15}}=2^{\frac{-3x}{2}}\ \to\ \dfrac{13x}{15}=\dfrac{-3x}{2}\ \to\ 26x=-45x\\\\ 26x+45x=0\ \to\ 66x=0\ \to\ \boxed{x=0}$