Problem: Simplify: Simplify: \left(\sqrt[3]{\sqrt[6]{a^{9}}} \right)^{4} \left( \sqrt[6]{\sqrt[3]{a^{9}}} \right)^
Answer Choices:
A. a16a^{16}a16 B. a12\mathrm{a}^{12}a12 C. a8a^{8}a8 D. a4a^{4}a4 E. a2a^{2}a2 Solution:
a9(1/6)(1/3)4â‹…a9(1/3)(1/6)4=a2â‹…a2=a4a^{9(1 / 6)(1 / 3) 4} \cdot a^{9(1 / 3)(1 / 6) 4}=a^{2} \cdot a^{2}=a^{4}a9(1/6)(1/3)4â‹…a9(1/3)(1/6)4=a2â‹…a2=a4.