The answer would be: B, C and D
The [tex] \frac{1}{4}[/tex] from [tex] \frac{1}{4} ^{3x^{2} }[/tex] can be converted into [tex] 4^{-1} [/tex] so it will be equal to [tex] 4^{-3x^{2} } [/tex]
The [tex] \frac{x}{4}[/tex] from [tex] \frac{x}{4} ^{3x }[/tex] can be converted into [tex] x^{1} [/tex] *[tex] 4^{-1} [/tex] so it will be equal to [tex] 4^{-3x^{2} } [/tex]
[tex] 4^{3x^{2} } [/tex] and [tex] 4^{-3x^{2} } [/tex] clearly not equivalent, so option A is out
