How do you simplify #(4x^5 (x^-1)^3)/((x^-2)^-2)#?

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Answer 1 · 2016-10-01T14:32:38

#(4x^5(x^(-1))^3)/(x^(-2))^(-2)=4/x^2#

We will use the identities #a^(-m)=1/a^m#, #(a^m)^n=a^((mxxn))# and #a^m*a^n=a^((m+n))#

Hence #(4x^5(x^(-1))^3)/(x^(-2))^(-2)#

= #(4x^5x^((-1)xx3))/(x^((-2)xx(-2))#

= #(4x^5x^(-3))/(x^4)#

= #(4x^5xx1)/(x^3xx x^4)#

= #(4x^5)/(x^(3+4)#

= #(4x^5)/x^7#

= #4/x^(7-5)#

= #4/x^2#