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The expression ((15625g^(2)y^(3))^(1/3)) * ((15625g^(2)y^(3))^(1/3)) equals kx^(r)y^(s)

where r, the exponent of g, is?
and s, the exponent of y, is?
and k, the leading coefficient is?


Jamey,  you didn't specify what you're supposed to do with the equation.  (Also, looks like a typo: should the "x" be "g"?)
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2 Answers

Hi Jamey,
My first step would be to distribute the cube root, or power of 1/3. If we do so, we get the (15625)^(1/3)=25, g^(2/3), and y^1. Now, we have two of these multiplied together, so we have 25g^(2/3)y*25g^(2/3)y. Using your knowledge of integer and exponential multiplication, you can combine these two expressions by multiplication. From there simply read the expression to get the k, s, and r you're looking for.
This is my solution for the problem.......
First lets ignore kgrys
Next lets simplify the other side of the expression: (15625g2y3)1/3 * (15625g2y3)1/3
Since the expressions are the same on either side of the multiplication sign, I am going to work with:
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:
Now is there anything that you can take the cubed root....yes
The cubed root of 15625 is 25 and the cubic root of y3 is y.
So that leaves you with the expression:
25y 3√g2
If you transform the cubed root of g2 to a fractional exponent you get:
Now lets put that back into the expression:
25yg2/3 * 25yg2/3 
or another way to write it is:
So now lets square the expression:
and rearrange:
So the answers are: