Question

What is the value of ${\left[\sqrt[3]{3\sqrt[6]{6a^9}}\right]}^4{\left[\sqrt[6]{6\sqrt[3]{3a^9}}\right]}^4$ ?

• A. $a^{16}$
• B. $a^{12}$
• C. $a^8$
• D. $a^4$

Answer 1

Answer: (D)

$a^4$

${\left(\sqrt[3]{3\sqrt[6]{6a^9}}\right)}^4{\left(\sqrt[6]{6\sqrt[3]{3a^9}}\right)}^4$

$={\left[a^{\frac{9}{6}\cdot \frac{1}{3}}\right]}^4{\left[a^{\frac{9}{3}\cdot \frac{1}{6}}\right]}^4$ $=a^2\cdot a^2=a^4$

Hence option 'D' is correct.