Pre-Calculus Help: Radical/Rational Exponents

[Confused Mike]

Hello Everyone! It's nice to meet you all here! Its good to know that there are people that can help those who are confused (or constantly confused like me) with math online. Anyways, I am currently within a chapter of my precalculus book where I have no clue what to do. The chapter is about simplifying radical and rational exponents

I was given eight problems, and I was able to make sense out of three of these...

The more complex problems had me stunned.

For example, "Simplify the Expression"

((3c)^(3/5) (2d)^(-2) (4c)^(1/2)) / ((4c)^(1/5) (2d)^(4) (2c)^(-3/2))

I have no idea where to start or where to finish with problems such as these.

If you can offer any assistance I would much appreciate it! Thanks![/b]

 

[Gene]

One way is to move everything into the numerator
((3c)^(3/5) (2d)^(-2) (4c)^(1/2)) / ((4c)^(1/5) (2d)^(4) (2c)^(-3/2)) =
((3c)^(3/5) (2d)^(-2) (4c)^(1/2)) ((4c)^(-1/5) (2d)^(-4) (2c)^(3/2)) =
Then split each term into a constant and variable
3^.6*c^.6*2^-2*d^-2*4^.5*c^.5*4^.2*c^.2*2^-4*d^-4*2^1.5*c^1.5 =
gather each term with all its exponents
3^(.6)*c^(.6+.5+.2+1.5)*2^(-2+1+.4-4+1.5)*d^(-2-4) =
3^.6*2^-3.1*c^2.8*d^-6

 

[Confused Mike]

Thank you so much for the help! I really appreciate the step by step walk through as well! I understand this a lil better now...I can almost guarentee I'll be back for more help in the future now! Thanks again!