1. (3x^4)^2 = 6x^8 wrong as explained by HighSchoolCalculus.
2. (3x^2y^4)(-2y^-8) = 9xy^4256y
I will work this one through slowly for you then maybew you can present the answers again and someone will check them for you :)
\((3x^2y^4)(-2y^{-8})\\ =3x^2y^4\times-2y^{-8}\\ =3\times x^2\times y^4\times-2\times y^{-8}\\ =3\times-2\times x^2\times y^4\times y^{-8}\\ =-6\times x^2\times y^{4+-8}\\ =-6\times x^2\times y^{-4}\\ =\frac{-6\times x^2\times y^{-4}}{1}\\ =\frac{-6\times x^2}{y^{+4}}\\ =\frac{-6x^2}{y^{4}}\\ \)
3. -4/x^-6 = -4x^6 correct
4. (x^-2y^-4)^-3(y^4y^3) = x^6y^19 correct
\( (x^{-2}y^{-4})^{-3}(y^4y^3) = x^6y^{19} \)
5. (x^2y^4)^4/(y^-2)^4 = x^6y^2
\((x^2y^4)^4/(y^{-2})^4 = x^6y^2\qquad wrong \)
? 6. (16x^2y^-4z^-1)^0/y^2 = 3/y^2 ? wrong - Anything (except 0) raised to the power of 0 is 1
a = -2 b=6 huh?
7. (3ab^-1)^2 = 9a^2b wrong
? 8.(4a^2b^-4)^0 ?
9.(x^5)^0=1 correct
?10.(a^2b^3)(missing exponent) = 1/a^2b^3 ?
11. x^-5*x^11=x^6 correct
12.w^8/w^5 = w^3 correct