Start by swapping the variables in the equations with their units (leave A alone for now): [tex] v=\frac{a^2t^A}{x} \Rightarrow \frac{L}{T} = \frac{ (\frac{L}{T^2})^2 T^A }{L} [/tex]
Multiply by L and square the fraction: [tex] \frac{L^2}{T} = \frac{L^2}{T^4} T^A \Rightarrow \frac{L^2}{T} \div \frac{L^2}{T^4}=T^A [/tex]
Divide the fraction by multiplying by the reciprocal: [tex] \frac{L^2}{T} \times \frac{T^4}{L^2} = T^A \Rightarrow T^3=T^A [/tex]
Therefore A=3
