Question

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

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

Answer 1

The correct option is B $5^4$

Given, ${\left(\sqrt[3]{3\sqrt[6]{65^9}}\right)}^4.{\left(\sqrt[6]{6\sqrt[3]{35^9}}\right)}^4$

${\left(\sqrt[3]{3\sqrt[6]{65^9}}\right)}^4.{\left(\sqrt[6]{6\sqrt[3]{35^9}}\right)}^4$$=5^{9\times \frac{1}{6}\times \frac{1}{3}\times 4}.5^{9\times \frac{1}{6}\times \frac{1}{3}\times 4}$$\dots (a^m{)}^n=a^{m\times n}$

$=5^2.5^2$$\dots (a^m.a^n=a^{m+n})$

$=5^4$

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