Question 1089763
<font color="black" face="times" size="3">There are many ways to do this. One such way is


{{{((6x^3)/(3x^4))^2=((6x^3)^2)/((3x^4)^2)}}}


{{{((6x^3)/(3x^4))^2=((6x^3)(6x^3))/((3x^4)(3x^4))}}}


{{{((6x^3)/(3x^4))^2=((6*6)(x^3*x^3))/((3*3)(x^4*x^4))}}}


{{{((6x^3)/(3x^4))^2=(36x^(3+3))/(9x^(4+4))}}}


{{{((6x^3)/(3x^4))^2=(36x^6)/(9x^8)}}}


{{{((6x^3)/(3x^4))^2=(9*4x^6)/(9x^8)}}}


{{{((6x^3)/(3x^4))^2=(highlight(9)*4x^6)/(highlight(9)x^8)}}}


{{{((6x^3)/(3x^4))^2=(cross(9)*4x^6)/(cross(9)x^8)}}}


{{{((6x^3)/(3x^4))^2=(4x^6)/(x^8)}}}


{{{((6x^3)/(3x^4))^2=(4x^6)/(x^6*x^2)}}}


{{{((6x^3)/(3x^4))^2=(4*highlight(x^6))/(highlight(x^6)*x^2)}}}


{{{((6x^3)/(3x^4))^2=(4*cross(x^6))/(cross(x^6)*x^2)}}}


{{{((6x^3)/(3x^4))^2=(4)/(x^2)}}}


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Or another method is this


{{{((6x^3)/(3x^4))^2=((3*2x^3)/(3x^4))^2}}}


{{{((6x^3)/(3x^4))^2=((highlight(3)*2x^3)/(highlight(3)x^4))^2}}}


{{{((6x^3)/(3x^4))^2=((cross(3)*2x^3)/(cross(3)x^4))^2}}}


{{{((6x^3)/(3x^4))^2=((2x^3)/(x^4))^2}}}


{{{((6x^3)/(3x^4))^2=((2x^3)/(x^3*x))^2}}}


{{{((6x^3)/(3x^4))^2=((2*highlight(x^3))/(highlight(x^3)*x))^2}}}


{{{((6x^3)/(3x^4))^2=((2*cross(x^3))/(cross(x^3)*x))^2}}}


{{{((6x^3)/(3x^4))^2=(2/x)^2}}}


{{{((6x^3)/(3x^4))^2=(2^2)/(x^2)}}}


{{{((6x^3)/(3x^4))^2=(4)/(x^2)}}}


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Whichever method you choose, the final simplified answer is {{{(4)/(x^2)}}}


Note: throughout all of this, x cannot equal zero


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