Generalize to non-dimensional formula

I try to solving dimensionless problem as you can see from image.

There are three different dimensionless group(x1,y1,z1) (x2,y2,z2) and (x3,y3,z3).

I can find the corresponding values by using matlab. But I want to use while or for loop for general formula in case of adding other variable.

As can be seen from the matlab codes I use same formulas for each three dimensionless but it is long for solution I want to use only one group codes and repeat for others by this way using shorter codes I want to reach solution. Thank you.

clear all;clc;

syms M L T A
syms X Y Z X1 Y1 Z1 X2 Y2 Z2 integer
syms X3 Y3 Z3 X4 Y4 Z4 X5 Y5 Z5 integer
ds= L;
u=L*T^-1;
v=L^2*T^-1;
U=L*T^-1;
d= L;
g=L*T^-2;
p=M*L^-3;



A=v;
eqn = (u)^X1 * (d)^Y1 * (p)^Z1 * (A) == M^0*L^0*T^0;

seqn = simplify(lhs(eqn)) == simplify(rhs(eqn));
collect(lhs(seqn),T);
powers = findSymType(ans, 'power');
need_to_solve = arrayfun(@(expression) children(expression,2), powers);
syms X2 Y2 Z2 %remove assumptions;
sol =solve(need_to_solve);
X1 = double(sol.X1)
Y1 = double(sol.Y1)
Z1 = double(sol.Z1)



A=U;
eqn = (u)^X2 * (d)^Y2 * (p)^Z2 * (A) == M^0*L^0*T^0;

seqn = simplify(lhs(eqn)) == simplify(rhs(eqn));
collect(lhs(seqn),T);
powers = findSymType(ans, 'power');
need_to_solve = arrayfun(@(expression) children(expression,2), powers);
syms X2 Y2 Z2 %remove assumptions;
sol =solve(need_to_solve);
X2 = double(sol.X2)
Y2 = double(sol.Y2)
Z2 = double(sol.Z2)

A=g;
eqn = (u)^X3 * (d)^Y3 * (p)^Z3 * (A) == M^0*L^0*T^0;

seqn = simplify(lhs(eqn)) == simplify(rhs(eqn));
collect(lhs(seqn),T);
powers = findSymType(ans, 'power');
need_to_solve = arrayfun(@(expression) children(expression,2), powers);
syms X3 Y3 Z3 %remove assumptions;
sol =solve(need_to_solve);
X3 = double(sol.X3)
Y3 = double(sol.Y3)
Z3 = double(sol.Z3)