Can you solve this please?

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Answer 1 · 2018-04-18T13:45:58

#((ab^(-5)-a^(-5)b)^(-1)(a^(-3)+b^(-3)))/(a^(-1)b^(-4)-b^(-1)a^(-4))^(-1)=1/(a^2b^2)#

#((ab^(-5)-a^(-5)b)^(-1)(a^(-3)+b^(-3)))/((a^(-1)b^(-4)-b^(-1)a^(-4))^(-1)#

= #((a/b^5-b/a^5)^(-1)(1/a^3+1/b^3))/((1/(ab^4)-1/(ba^4))^(-1)#

= #(((a^6-b^6)/(a^5b^5))^(-1)((b^3+a^3)/(a^3b^3)))/((a^3-b^3)/(a^4b^4))^(-1)#

= #(a^5b^5)/(a^6-b^6) * (a^3+b^3)/(a^3b^3)*(a^3-b^3)/(a^4b^4)#

= #a^((5-4-3))b^((5-4-3))*((a^3+b^3)(a^3-b^3))/((a^3+b^3)(a^3-b^3)#

= #a^(-2)b^(-2)#

= #1/(a^2b^2)#