# Simplify. (2x^-3y^4)^3 (6x^8y^-15) (4x^2y)/(3xy)^2 (8x^-9y^7)

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Simplify `((2x^-3y^4)^3 (6x^8y^-15) (4x^2y))/((3xy)^2 (8x^-9y^7))`:

First eliminate the parentheses using `(ab)^x=a^xb^x`

`=(8*x^(-9)y^12*6x^8y^(-15)*4x^2y)/(9x^2y^2*8x^(-9)y^(7))`

Now use `a^x*a^y=a^(x+y)` in both numerator and denominator:

`=(192x^(-9+8+2)y^(12-15+1))/(72x^(2-9)y^(2+7))`

`=(192x^1y^(-2))/(72x^(-7)y^9)`

Now use `a^x/a^y=a^(x-y)` :

`=(192/72)(x^(1-(-7)))(y^(-2-9))`

`=(8/3)x^8y^(-11)`

Now use `a^(-x)=1/a^x`

`=(8x^8)/(3y^(11))`

Which is fully simplified.