Question

Compute the following
$\sqrt[3]{35^{\frac{1}{{\log }_{7}5}+\frac{1}{(-{\log }_{10}0.1)}}}$

Answer 1

${(\frac{1}{5^{lo{g}_7^5}}+\frac{1}{(-lo{g}_{10}^{0.1/10})})}^{1/3}$

${(\frac{1}{7}+\frac{1}{1})}^{1/3}={\left(\frac{8}{7}\right)}^{1/3}=\frac{2}{7^{1/3}}$.