Question

Simplify $\left(\sqrt[2]{2\sqrt[6]{65^9}}{)}^4\right(\sqrt[6]{6\sqrt[3]{35^4}}{)}^4$

• A. $5^{\frac{17}{9}}$
• B. $5^{\frac{35}{9}}$
• C. $25$
• D. $1$

Answer 1

The correct option is B $5^{\frac{35}{9}}$

${\left(\sqrt[2]{2\sqrt[6]{65^9}}\right)}^4.{\left(\sqrt[6]{6\sqrt[3]{35^4}}\right)}^4={\left(\sqrt[2]{25^{\left(\frac{9}{6}\right)}}\right)}^4.{\left(\sqrt[6]{65^{\left(\frac{4}{3}\right)}}\right)}^4={\left(5^{\left(\frac{3}{4}\right)}\right)}^4.{\left(5^{\left(\frac{2}{9}\right)}\right)}^4=5^3{.5}^{\left(\frac{8}{9}\right)}=5^{3+\left(\frac{8}{9}\right)}=5^{\left(\frac{35}{9}\right)}$