# ACT Math 4.2 Pre-Algebra

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

ACT Math | Pre-Algebra |

ACT Mathematics | Pre-Algebra |

Algebra | Sequences and Series |

Foreign Language | Arabic Subtitled Chinese Subtitled Korean Subtitled Spanish Subtitled |

Intermediate Algebra | Sequences and patterns |

Language | English Language |

Pre-Algebra | Series |

Product Type | ACT Math |

### Transcript

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."