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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 \(\sqrt[a]{b}\)
+2407 Hello!
I love your pfp :))
So, lets turn everything where the base is 2.
2^(1/3) is already in base 2.
4^(1/9) = (2^2)^(1/9) = 2^(2/9)
8^(1/27) = (2^3)^(1/27) = 2^(3/27) = 2^(1/9)
16^(1/81) = (2^4)^(1/81) = 2^(4/81)
Now that everything is in base 2, we can just add. :))
1/3+2/9+1/9+4/81 = 58/81
2^(58/81) = <81>sqrt(2^58)
I hope this helped. :))
=^._.^=
