SOLUTION: Need assistance please. Really, really lost. More than anything I would like to understand how to come to the solution. I have been working on this for quite some time. [(3x^4)/

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Need assistance please. Really, really lost. More than anything I would like to understand how to come to the solution. I have been working on this for quite some time. [(3x^4)/      Log On


   



Question 1123069: Need assistance please. Really, really lost. More than anything I would like to understand how to come to the solution. I have been working on this for quite some time.
[(3x^4)/(2y^-3)]^-3
Simplify using positive exponents only.
Thank you!

Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
%28%283x%5E4%29%2F%282y%5E%28-3%29%29%29%5E%28-3%29

First give the coefficient numbers 3 and 2 the exponent 1:

%28%283%5E1x%5E4%29%2F%282%5E1y%5E%28-3%29%29%29%5E%28-3%29

Now that every factor has an exponent, we remove the parentheses,
by multiplying every exponent inside the parentheses by the exponent
outside the parentheses.  [This is the distributive principle of
exponents],



Simplify:

%283%5E%28-3%29x%5E%28-12%29%29%2F%282%5E%28-3%29y%5E9%29

Now use the rule for making negative exponents positive, which is

If there is a negative exponent on the TOP, move the base and
exponent to the BOTTOM and change the sign of the negative
exponent to positive.

and 

If there is a negative exponent on the BOTTOM, move the base and
exponent to the TOP and change the sign of the negative
exponent to positive.

So we move the 3-3 from the top to the bottom and put 33 on the bottom.

We move the x-12 from the top to the bottom and put x12 on the bottom.  

And we move the 2-3 from the bottom to the top and put 23 on the top.

But we leave the y9 on the bottom because it already
has a positive exponent.

%282%5E3%29%2F%283%5E3x%5E12y%5E9%29

We finish by raising 2 to the 3 power and getting 2∙2∙2 = 8,
and raising 3 to the 3 power and getting 3∙3∙3 = 27:

8%2F%2827x%5E12y%5E9%29

Edwin

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(3x^4/2y^-3)^-3
Simplify using positive exponents only.
(3x^4/2y^-3)^-3
The order of the steps does not matter.
(3x^4/2y^-3)^-3
Multiply exponents by the -3
= (27x^-12)/8y^9
Multiply NUM and DEN by x^12
= 27%2F8x%5E12y%5E9
------------
If you prefer:
= %283%2F%282x%5E4y%5E3%29%29%5E3