Consider the equation . the dimensions of the variables v, x, and t are , , and , respectively. the numerical factor 3 is dimensionless. what must be the dimensions of the variable z, such that both sides of the equation have the same dimensions?

Part of the question is missing but here is the equation for the function;

Consider the equation v = (1/3)zxt2. The dimensions of the variables v, x, and t are [L/T], [L], and [T] respectively.

Answer = The dimension for z = 1/T3 i.e 1/ T - raised to power 3

Explanation:

What is applied is the principle of dimensional homogenuity

From the equation V = (1/3)zxt2.

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle