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ACT Math 4.2 Pre-Algebra 390 Views


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Description:

ACT Math: Pre-Algebra Drill 4, Problem 2. What is the fourth term in the series?

Language:
English Language

Transcript

00:03

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

00:07

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

00:10

Each subsequent term is determined as the

00:12

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

00:16

And here are the potential answers...

00:22

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

00:25

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

00:28

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

00:33

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

00:37

raised to the one half power.

00:40

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

00:44

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

00:47

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

00:52

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

00:57

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

01:01

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

01:06

as the second term.

01:08

Now do it again to get the 3rd term.

01:10

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

01:16

three-halves, or 9/8.

01:18

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

01:24

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

01:33

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

01:40

As in, "Exponentland."

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