Question

Find the exponent A in the equation

Answer 1

Start by swapping the variables in the equations with their units (leave A alone for now): $v=\frac{a^2t^A}{x} \Rightarrow \frac{L}{T} = \frac{ (\frac{L}{T^2})^2 T^A }{L}$

Multiply by L and square the fraction: $\frac{L^2}{T} = \frac{L^2}{T^4} T^A \Rightarrow \frac{L^2}{T} \div \frac{L^2}{T^4}=T^A$

Divide the fraction by multiplying by the reciprocal: $\frac{L^2}{T} \times \frac{T^4}{L^2} = T^A \Rightarrow T^3=T^A$

Therefore A=3