SOLUTION: what is a to the -1 half divided by 6a to 1 third times a to the -1 fourth look like when simplified?

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Question 541919: what is a to the -1 half divided by 6a to 1 third times a to the -1 fourth look like when simplified?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
a to the -1 half divided by 6a to 1 third times a to the -1 fourth look 
I can't tell if you mean this

matrix%283%2C1%2C%22%22%2C%28a%5E%281%2F2%29%29%2F%286a%5E%281%2F3%29%29%2C%22%22%29++·matrix%283%2C1%2C%22%22%2Ca%5E%281%2F4%29%2C%22%22%29or this:  

If it's this one:

matrix%283%2C1%2C%22%22%2C%28a%5E%281%2F2%29%29%2F%286a%5E%281%2F3%29%29%2C%22%22%29++·matrix%283%2C1%2C%22%22%2Ca%5E%281%2F4%29%2C%22%22%29

write the expression matrix%283%2C1%2C%22%22%2Ca%5E%281%2F4%29%2C%22%22%29 as matrix%283%2C1%2C%22%22%2C%28a%5E%281%2F4%29%29%2F1%2C%22%22%29, then you have:

matrix%283%2C1%2C%22%22%2C%28a%5E%281%2F2%29%29%2F%286a%5E%281%2F3%29%29%2C%22%22%29++·matrix%283%2C1%2C%22%22%2C%28a%5E%281%2F4%29%29%2F1%2C%22%22%29


Indicate the multiplication of the numerators and multiplication of
denominators



Add the exponents in the top 1%2F2+1%2F4 = 2%2F4+1%2F4 = 3%2F4

matrix%283%2C1%2C%22%22%2C%28a%5E%283%2F4%29%29%2F%286a%5E%281%2F3%29%29%2C%22%22%29+


Subtract the exponents 3%2F4-1%2F3 = 9%2F12-5%2F12 = 5%2F12

matrix%283%2C1%2C%22%22%2Ca%5E%285%2F12%29%2F6%2C%22%22%29which can also be written in root form:

1%2F6root%2812%2Ca%5E5%29 

------------------------

However, if it's this:



Add the exponents on the bottom:  1%2F3%2B1%2F4=4%2F12%2B3%2F12=7%2F12

matrix%283%2C1%2C%22%22%2Ca%5E%281%2F2%29%2F%286a%5E%287%2F12%29%29%2C%22%22%29++

Subtract the exponents 1%2F2+-+7%2F12=6%2F12-7%2F12 = -1%2F12

matrix%283%2C1%2C%22%22%2Ca%5E%28-1%2F12%29%2F6%2C%22%22%29++


Move the negative exponential from the top to the bottom:

matrix%283%2C1%2C%22%22%2C1%2F%286a%5E%281%2F12%29%29%2C%22%22%29++

Write the denominator in root form

1%2F%286%2Aroot%2812%2Ca%29%29

Edwin