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\(\sqrt[a]{b}.\)

Thanks for your time! :)

By Mathematica, the product is Prod[(2^n)^{1/3^n}, n = 1, n = n + 1, n <= inf], which spits out \(\sqrt[3]{4}\), or \sqrt[3]{4}.

∏ [ (2^n)^(3^-n), n, 1, ∞ ] =2^(3/4) =(2^3)^(1/4)

My attempt is as follows:

Edit: common ratio should be lambda^-1; the RHS of the second equation on the line beginning "hence" should have a 1 in the numerator not a lambda.