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It's howdy-shmoopy time... It's howdy-shmoopy time...

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The first term in a series is the square root of x.

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Each subsequent term is determined as the

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previous term raised to the power of three-halves. What is the fourth term?

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And here are the potential answers...

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Ugh. This one is... ugly. But maybe it's

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pretty on the inside. Let's think this one through.

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In any question where we have both a fraction AND a square root sign, odds are good that

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they are testing us on whether or not we realize that a square root is just the inside part

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raised to the one half power.

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That is, the square root of x here is the same as x to the one half.

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So... now that we are all living in Exponentland...

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We have a series of 4 terms... and term 1 here is x to the one half.

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Now we raise the power to three-halves for the second term -- and we know -- hopefully

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-- that if we are raising exponents to powers we just multiply the exponents...

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...so in this case we multiply one half by three halves to get x to the three-fourths

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as the second term.

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Now do it again to get the 3rd term.

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We have x to the three-fourths to the power 3 over 2, which is multiplied to get 3/4 times

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three-halves, or 9/8.

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Almost to the promised land... located conveniently between Exponentland and Frontierland...

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Ok... we have x to the 9/8 to the three-halves, so we multiply 9 over 8 by 3 over 2 to get

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27 over 16... or x to the 27/16ths... and the answer is E.

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As in, "Exponentland."

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