There exists notation for the pointwise multiplication of a function $j$ or $k$. This is often denoted as $j\cdot k$ or $j \circ k$ using the Hadamard notation. Consider the pointwise exponentiation of some function $f:X \rightarrow Y$ with exponent $n$ denoted by $g:Y\rightarrow Z$:
$$Z = \left\{x_i \in X|f(x_i)^{n}\right\}$$
How can the operation of pointwise exponentiation be notated? Does $g = f^n$ suffice? For instance in the programming language Matlab this operation would be expressed as
X.^n to distinguish it from X^n which denotes matrix multiplication.