This is my solution for the problem.......
First lets ignore kg^{r}y^{s}
Next lets simplify the other side of the expression: (15625g^{2}y^{3})^{1/3} * (15625g^{2}y^{3})^{1/3}
Since the expressions are the same on either side of the multiplication sign, I am going to work with:
(15625g^{2}y^{3})^{1/3}
A fractional exponent is a short hand way of writing roots. In this particular instance we are dealing with a cubic root. So you can rewrite the expression like this:
3√15625g^{2}y^{3 }
Now is there anything that you can take the cubed root....yes
The cubed root of 15625 is 25 and the cubic root of y^{3} is y.
So that leaves you with the expression:
25y 3√g^{2}
If you transform the cubed root of g^{2} to a fractional exponent you get:
25yg^{2/3}
Now lets put that back into the expression:
25yg^{2/3} * 25yg^{2/3}
or another way to write it is:
(25yg^{2/3})^{2}
So now lets square the expression:
625y^{2}g^{4/3}
and rearrange:
625g^{4/3}y^{2}
So the answers are:
k=625
r=4/3
s=2
Sep 1

Laura J.
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