solution: Note that $a^2 = 64$ and $\sqrt[3]{64} = 4$. Therefore, $$\left(16\sqrt[3]{a^2}\right)^{\frac {1}{3}} = \left(16 \times 4\right)^{\frac{1}{3}} = 64^\frac{1}{3} = \boxed{4}.$$
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  If $a = 8$, what is the value of $\left(16\sqrt[3]{a^2}\right)^{\frac 13}$?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 4
extra_info.question: If $a = 8$, what is the value of $\left(16\sqrt[3]{a^2}\right)^{\frac 13}$?
extra_info.split: test