SOLUTION: Please help- I have started the problem, just not sure I am going down the right road.... Raise the quantity in parentheses to the indicated exponent, and simplify the resulting

Question 601287: Please help- I have started the problem, just not sure I am going down the right road....
Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression. Express answers with positive exponents.
(24y^-1/72x^-3y^4)^2
Here is what I have so far!
72/24=3
(y^-1/3x^-3y^4)^2
(y^-1/3x^-3y^4)^2* y^-4 (which leaves y^-4*y^-1= y^4)
(y^4/3x^-3)^2
PLEASE HELP!!!!!!!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You should have (y^-5/3x^-3)^2 because (y^-1)/(y^4) = y^(-1-4) = y^(-5)

Now square both the numerator and denominator separately

Square the numerator: (y^(-5))^2 = y^(-5*2) = y^(-10)

So the new numerator is now y^(-10). To write the exponent as a positive number, you flip the base to get 1/(y^10)

-------------------------------------------------------
Square the denominator: (3x^-3)^2 = 3^2*x^(-3*2) = 9x^-6

So the new denominator is now 9x^-6

Finally, flip the base that has the negative exponent to get 9/(x^6)

So combine the new numerator and denominator to get

(1/(y^10))/(9/(x^6)) = (1/(y^10))*(x^6)/9 = (x^6)/(9y^10)

Giving you the final answer of (x^6)/(9y^10)

================================================================================
Answer:

So $\left(\frac{24y^{-1}}{72x^{-3}y^4}\right)^2$ completely simplifies to $\frac{x^6}{9y^{10}}$

In other words $\left(\frac{24y^{-1}}{72x^{-3}y^4}\right)^2 = \frac{x^6}{9y^{10}}$ for all allowed values of x and y.

RELATED QUESTIONS
This is my last problem on this assignment and I can't figure the thing out, HELP... (answered by jim_thompson5910)

3*4^2-2^3-3^2=23 We were asked to put grouping symbols in this problem to make it... (answered by macston)

I am not exactly sure if this is a linear equation but I need help!!! I am... (answered by solver91311)

I have solved this problem, but I doubt if I did this in the correct manner or even if... (answered by richwmiller)

Please help, I am not sure how to do this two problem Remove the parentheses in each of... (answered by checkley71)

I have the solutions to this problem from the back of my book. I just don't know how to... (answered by edjones)

Raise the quantity in Parentheses to the indeicated exponent, and simplify the resulting... (answered by solver91311)

I have apparently become to reliant on my calculator. I am not sure how to show the work... (answered by ankor@dixie-net.com)

I am unable to do this problem. Please help! raise the quantity in parenthesis to... (answered by mananth)