How do you simplify #[(2x^-3 * y^-1) / (4x^-5 * y^-4)]^2 * [(8x^5 * y^6) / (4x^7 * y^4)]^3#?

1 Answer
Oct 11, 2017

Answer:

#2x^-2y^12 or (2y^12)/x^2#

Explanation:

#[(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#