Final answer:
The question seems to contain typos and lacks clarity, making it impossible to provide a simplified form of the expression. Dimensional analysis ensures each term in the equation has the same dimension.
Step-by-step explanation:
The question seems to be asking for the simplified form of the given expression T : m 3 : 8 m : w 4 : 7 t : m : w, but unfortunately, the expression provided appears to have typographical errors and lacks clarity. Given the information provided, we're unable to determine the exact expression and therefore cannot simplify it. However, if the question is related to dimensional analysis, which the context seems to suggest with dimensions like [m], [s], [v], [a], and [t], it's important to ensure that each term in an equation has the same dimension. For example, in the equations F = ma, K = 0.5mv², and W = mas, each side of the equation is dimensionally consistent.