Question 531014
I'll do the first three to get you started


# 1


Use the idea that {{{root(n,x^n)=abs(x)}}} where n is even



So


{{{root(12, (-5)^12) = abs(-5) = 5}}}



or simply 



{{{root(12, (-5)^12) = 5}}}


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# 2



(-3x)^2(2x^8)^2



(-3)^2*(x^2)(2)^2*(x^8)^2



9x^2*4*x^16



36x^18



So (-3x)^2(2x^8)^2 = 36x^18


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# 3


(3x^3-4)(x^6-1)



(3x^3)(x^6)+(3x^3)(-1)+(-4)(x^6)+(-4)(-1)



3x^9-3x^3-4x^6+4



So (3x^3-4)(x^6-1)=3x^9-3x^3-4x^6+4