Using Properties of exponents

[Mackenzie25]

In this problem, I'm supposed to simplify the expression step-by-step, and I'm not quite sure where I'm doing it wrong, but I'm coming up with the wrong answer. If anyone knows how to help me solve this, it would be fantastic! My apologies for the set-up of the problem, I'm not the best with all of the codes.
Thanks in advance!
~Mackenzie

Simplify the following expression:
((y[sup:2wyliok4]6[/sup:2wyliok4])6x[sup:2wyliok4]4[/sup:2wyliok4]) * ((18x)/x[sup:2wyliok4]2[/sup:2wyliok4]y)

I multiplied across the problem, and ended up with:
y[sup:2wyliok4]6[/sup:2wyliok4]18x
_____________
6x[sup:2wyliok4]4+2[/sup:2wyliok4]y

I switched the two variables for x and y in the numerator, and solved for the exponent in the denominator.
18x y[sup:2wyliok4]6[/sup:2wyliok4]
_____________
6x[sup:2wyliok4]6[/sup:2wyliok4]y

From here, I get a little stuck, so I think this is where my mistake is.

3x y[sup:2wyliok4]6[/sup:2wyliok4]
_____________
x[sup:2wyliok4]6[/sup:2wyliok4]y

3x[sup:2wyliok4]1-6[/sup:2wyliok4]y[sup:2wyliok4]6-1[/sup:2wyliok4]

3x[sup:2wyliok4]-5[/sup:2wyliok4]y[sup:2wyliok4]5[/sup:2wyliok4]
This is about as far as I got....

 

[wjm11]

((y^6)/6x^4) * ((18x)/x^2y)
= 3(x^-5)(y^5)

Your work is correct. Good job.

Sometimes it is required to give the answer without any negative exponents. Just move the x term to the denominator and change the sign:

3(x^-5)(y^5) = 3(y^5)/(x^5)

 

[wjm11]

((y^6)/6x^4) * ((18x)/x^2y)
= 3(x^-5)(y^5)

Your work is correct. Good job.

Sometimes it is required to give the answer without any negative exponents. Just move the x term to the denominator and change the sign:

3(x^-5)(y^5) = 3(y^5)/(x^5)

 

[Mackenzie25]

Thanks!