[tex]A.\ 4^x\cdot4^x=4^{x+x}=4^{2x}\qquad\text{used}\ a^n\cdot a^m=a^{n+m}\\\\B.\ 4^{2x}=(4^2)^x=16^x\qquad\text{used}\ (a^n)^m=a^{nm}\\\\C.\ 4^2\cdot4^x=4^{2+x}\\\\D.\ (4\cdot4)^x=16^x\\\\E.\ 4\cdot4^{2x}=4^{1+2x}\\\\F.\ 4\cdot4^x=4^{1+x}\\\\Answer:\ \boxed{B.\ and\ D.}[/tex]
