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

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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.
 
Cheers,
Jess
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:
 
(15625g2y3)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√15625g2y3   
 
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:
 
25yg2/3
 
 
Now lets put that back into the expression:
 
25yg2/3 * 25yg2/3 
 
or another way to write it is:
 
(25yg2/3)2
 
So now lets square the expression:
 
625y2g4/3
 
and rearrange:
 
625g4/3y2
 
 
So the answers are:
 
k=625
r=4/3
s=2