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

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Answer 1 · 2016-06-16T10:21:41

#= 4/x^2#

Use the power law of indices.. "Multiply the indices".

#(4x^5(x^-3))/(x^4) " now simplify"#

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

#= 4/x^2#

OR, you could deal with the negative index first by moving it to the denominator so the index is positive.

#(4x^5)/(x^4 xx x^3) = (4x^5)/x^7#

#= 4/x^2#

Which method you use is entirely your choice, one is not better than the other.

Answer 2 · 2016-06-16T10:22:29

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

We use the identities #(a^m)^n=a^(mxxn)#, #a^mxxa^n=a^(m+n)# 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^(5-3-4)#

= #4x^(-2)#

= #4/x^2#