#[(2x^-3 cdot y^-1)/(4x^-5 cdot y^-4)]^2 cdot [(8x^5 cdot y^6)/(4x^7 cdot y^4)]^3#
Simplifying the coefficients first..
#[(cancel(2)^1x^-3 cdot y^-1)/(cancel(4)^2x^-5 cdot y^-4)]^2 cdot [(cancel(8)^2x^5 cdot y^6)/(cancel(4)^1x^7 cdot y^4)]^3#
#[(x^-3 cdot y^-1)/(2x^-5 cdot y^-4)]^2 cdot [(2x^5 cdot y^6)/(x^7 cdot y^4)]^3#
Using Indices..
Recall; #rArr x^a/x^b = x^(a - b)#
#[(1/2x^(-3 - (-5)) cdot y^(-1 - (-4)))]^2 cdot [(2x^(5 - 7) cdot y^(6 - 4))]^3#
Simplifying the indexes..
#[(1/2x^(-3 + 5) cdot y^(-1 + 4))]^2 cdot [(2x^-2 cdot y^2)]^3#
#[(1/2x^2 cdot y^3)]^2 cdot [(2x^-2 cdot y^2)]^3#
Multiplying the indexes to their respective brackets..
#((1/2)^2x^(2 xx 2) cdot y^(3 xx 2)) cdot 2^3x^(-2 xx 3) cdot y^(2 xx 3)#
#(1/4x^4 cdot y^6) cdot 8x^-6 cdot y^6#
#(1/cancel4_1x^4 cdot y^6) cdot cancel8^2x^-6 cdot y^6#
#x^4 cdot y^6 cdot 2x^-6 cdot y^6#
Using Indices..
Recall; #rArr x^a xx x^b = x^(a + b)#
#2x^(4 + (-6)) cdot y^(6 + 6)#
#2x^(4 - 6) cdot y^12#
#2x^-2y^12 or (2y^12)/x^2 -> Answer#
