efectuar.... Question from @Cherry97

Cherry97 @Cherry97

September 2019 1 14 Report

$\sqrt[3]{ \sqrt{( \sqrt[3]{512})( \sqrt[3]{216} + 2) } }$
efectuar

Caketheted

Respuesta:

Explicación paso a paso:

$\sqrt[3]{\sqrt{\left(\sqrt[3]{512}\right)\left(\sqrt[3]{216}+2\right)}}$

Aplicar la ley de exponentes: $\sqrt[n]{a}=a^{\frac{1}{n}}$

$=\left(\left(\sqrt[3]{512}\left(\sqrt[3]{216}+2\right)\right)^{\frac{1}{2}}\right)^{\frac{1}{3}}$

Aplicar la ley de exponentes: $\left(a^b\right)^c=a^{bc}$

$=\left(\sqrt[3]{512}\left(\sqrt[3]{216}+2\right)\right)^{\frac{1}{2}\cdot \frac{1}{3}}\\\\=\left(\sqrt[3]{512}\left(\sqrt[3]{216}+2\right)\right)^{\frac{1}{6}}$

Aplicar la ley de exponentes $a^{\frac{1}{n}}=\sqrt[n]{a}$

$=\sqrt[6]{\sqrt[3]{512}\left(\sqrt[3]{216}+2\right)}\\\\=\sqrt[6]{8\left(2+\sqrt[3]{216}\right)}\\\\=\sqrt[6]{8\left(6+2\right)}\\\\=\sqrt[6]{8\cdot \:8}\\\\=\sqrt[6]{64}\\\\=\sqrt[6]{2^6}\\\\=2$