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It’s howdy-shmoopy time… The first term in a series is the square
root of x. Each subsequent term is determined as the
previous term raised to the power of three-halves. What is the fourth term?
And here are the potential answers… Ugh. This one is… ugly. But maybe it’s
pretty on the inside. Let’s think this one through.
In any question where we have both a fraction AND a square root sign, odds are good that
they are testing us on whether or not we realize that a square root is just the inside part
raised to the one half power.
That is, the square root of x here is the same as x to the one half.
So... now that we are all living in Exponentland…
We have a series of 4 terms… and term 1 here is x to the one half.
Now we raise the power to three-halves for the second term – and we know – hopefully
– that if we are raising exponents to powers we just multiply the exponents…
…so in this case we multiply one half by three halves to get x to the three-fourths
as the second term.
Now do it again to get the 3rd term.
We have x to the three-fourths to the power 3 over 2, which is multiplied to get 3/4 times
three-halves, or 9/8.
Almost to the promised land… located conveniently between Exponentland and Frontierland…
Ok… we have x to the 9/8 to the three-halves, so we multiply 9 over 8 by 3 over 2 to get
27 over 16… or x to the 27 16ths… and the answer is E.
As in, “Exponentland.”