Radicals-> Exponential equations

rock4christ
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how would I take the cube root of the square root of 2 as an exponential equation? the square root of 2 is 21/2 but I don't know what to do with the cube root.
 
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The cubed root of x is x1/3. So, your expression for the cubed root of the square root of 2 is (2^{\frac{1}{2}})^{\frac{1}{3}}. Can you simplify this?
 
well Id have to simplify it, because I am supposed to turn the new simplified exponent to a radical
 
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Was that an answer to Cristo's question?? He asked do you know HOW to simplify it.
 
oh, no i don't know how
 
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I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

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