How do you simplify #(\frac { - x ^ { 4} y ^ { 4} \cdot - x ^ { - 2} y ^ { 3} } { - x y ^ { - 1} } ) ^ { 4}#?

1 Answer
Lucy
Jul 24, 2018

#x^4y^32#

Explanation:

#((-x^4y^4*-x^(-2)y^3)/(-xy^(-1)))^4#

Numerator:
#-x^4y^4*-x^(-2)y^3#
=#-x^4y^4times-y^3/x^2#
=#x^2y^7#

Denominator:
#-xy^(-1)#
=#-x/y#

Therefore,
#((-x^4y^4*-x^(-2)y^3)/(-xy^(-1)))^4# becomes #((x^2y^7)/(-x/y))^4#
=#((x^2y^7)times-y/x)^4#
=#(-xy^8)^4#
=#x^4y^32#

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