[tex]a.\\3(x^2)^6(2x^3)^4=3x^{2\cdot6}(2^4)(x^3)^4=3x^{12}(16)(x^{3\cdot4})\\\\=48x^{12}x^{12}=48x^{12+12}=48x^{24}\\\\\text{Used:}\\(a^n)^m=a^{nm}\\\\(ab)^n=a^nb^n[/tex]
[tex]b.\\5x^{5n}\cdot(-3x^2)=-(5\cdot3)x^{5n}x^2=-15x^{5n+2}\\\\\text{Used:}\\\\a^n\cdot a^m=a^{n+m}[/tex]
[tex]c.\\\dfrac{100b^{2n}}{-20b^5}=\dfrac{100}{-20}b^{2n-5}=-5b^{2n-5}\\\\\text{Used:}\\\\\dfrac{a^n}{a^m}=a^{n-m}[/tex]
