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

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Answer 1 · 2017-08-11T13:38:19

#x^-4*y^-12#

#(x^-4y^-2*x^2y^-4)^2#

#=>(x^-4y^-2*x^2y^-4)^2#

#a^n*a^m=a^(n+m),#multiplying as per this equation within the brackets.

#=>(x^-4*x^2*y^-2*y^-4)^2#

#=>(x^(-4+2)*y^(-2+ -4))^2#

#=>(x^-2*y^(-2-4))^2#

#=>(x^-2*y^-6)^2#

#(x^n)^m=x^(n*m),#so #(x^n*y^p)^m=x^(n*m)*y^(p*m),# from this we can simply the equation as#:#

#=>x^(-2*2)*y^(-6*2)#

#=>x^-4*y^-12#