Section: Mathematical Operators
y = a .^ b
The result y depends on which of the following three situations applies to the arguments a and b:
a is a scalar, b is an arbitrary n-dimensional numerical array, in which case the output is a raised to the power of each element of b, and the output is the same size as b.
 a is an n-dimensional numerical array, and b is a scalar, then the output is the same size as a, and is defined by each element of a raised to the power b.
 a and b are both n-dimensional numerical arrays of \emph{the same size}.  In this case, each element of the output is the corresponding element of a raised to the power defined by the corresponding element of b.
 typerules
for more details.
 
and the second form
 
and in the third form
 
--> a = 2 a = 2 --> b = 1:4 b = 1 2 3 4 --> c = a.^b c = 2 4 8 16
The second case shows a vector raised to a scalar.
--> c = b.^a c = 1 4 9 16
The third case shows the most general use of the dot-power operator.
--> A = [1,2;3,2]
A = 
 1 2 
 3 2 
--> B = [2,1.5;0.5,0.6]
B = 
    2.0000    1.5000 
    0.5000    0.6000 
--> C = A.^B
C = 
    1.0000    2.8284 
    1.7321    1.5157