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)/

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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)   (Show Source): You can put this solution on YOUR website!


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



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:



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.



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:



Edwin

Answer by Alan3354(69443)   (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
=
------------
If you prefer:
=

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