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

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