All the 3 first ways are identical. You have make sure that if t is a matrix you add . before using multiplication or the power.
for matrix:
t= [1 2 3;2 3 4;3 4 5];
tp=t.*t;
x=exp(-(t.^2));
y=exp(-(t.*t));
z=exp(-(tp));
gives the results:
x =
0.3679 0.0183 0.0001
0.0183 0.0001 0.0000
0.0001 0.0000 0.0000
y =
0.3679 0.0183 0.0001
0.0183 0.0001 0.0000
0.0001 0.0000 0.0000
z=
0.3679 0.0183 0.0001
0.0183 0.0001 0.0000
0.0001 0.0000 0.0000
And using a scalar:
p=3;
pp=p^2;
x=exp(-(p^2));
y=exp(-(p*p));
z=exp(-pp);
gives the results:
x =
1.2341e-004
y =
1.2341e-004
z =
1.2341e-004