Determine the value of the infinite product $(2^{1/3})(4^{1/9})(8^{1/27})(16^{1/81}) \dotsm.$  Enter your answer in the form "\sqrt[a]{b}", which stands for $\sqrt[a]{b}.$
Question:
Determine the value of the infinite product $(2^{1/3})(4^{1/9})(8^{1/27})(16^{1/81}) \dotsm.$  Enter your answer in the form "\sqrt[a]{b}", which stands for $\sqrt[a]{b}.$
Answer:
Let's think step by step.

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\sqrt[4]{8}
Determine the value of the infinite product $(2^{1/3})(4^{1/9})(8^{1/27})(16^{1/81}) \dotsm.$  Enter your answer in the form "\sqrt[a]{b}", which stands for $\sqrt[a]{b}.$
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