Show that for each infinite cardinal $\displaystyle \kappa$, $\displaystyle \kappa <_c \kappa^{\text{cf}(\kappa)}$.

Notation: $\displaystyle \text{cf}$ denotes the cofinality. I know some properties of $\displaystyle \text{cf}(\kappa)$. They may be helpful.

$\displaystyle \text{cf}(\kappa) \leq_c \kappa$

For each infinite cardinal number $\displaystyle \kappa$, $\displaystyle \text{cf}(2^{\kappa}) >_c \kappa$.

However, I do not see how to prove this. Any hints would be great. Thanks.