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