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

Question

where r, the exponent of g, is?

and s, the exponent of y, is?

and k, the leading coefficient is?

Answer 1

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

Answer 2

This is my solution for the problem.......

 

First lets ignore kg^ry^s

 

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:

 

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:

 

625y²g^4/3

 

and rearrange:

 

625g^4/3y²

 

 

So the answers are:

 

k=625

r=4/3

s=2