Question

Evaluate: ${\left[\sqrt[3]{3\sqrt[6]{65^9}}\right]}^4{\left[\sqrt[6]{6\sqrt[3]{35^9}}\right]}^4$

• A. $5^2$
• B. $5^4$
• C. $5^8$
• D. $5^{12}$

Answer 1

The correct option is B $5^4$

${\left[\sqrt[3]{3\sqrt[6]{65^9}}\right]}^4\times {\left[\sqrt[6]{6\sqrt[3]{35^9}}\right]}^4$

$=5^{9\times \frac{1}{6}\times \frac{1}{3}\times 4}\times 5^{9\times \frac{1}{3}\times \frac{1}{6}\times 4}$

$=5^2\times 5^2=5^4$