elementary set theory - Equinumerousity of operations on cardinal numbers

I want to prove for all Cardinal numbers $a$, $b$, $c$ that:

1. 
   
   

   $(a \cdot b)^c =_c a^c \cdot b^c$

   
   


2. 
   

   $a^{(b+c)} =_c a^b \cdot a^c$

   
   


3. 
   

   $(a^b)^c =_c a^{b \cdot c}$

   
   

I know that for 1. it's enough to show that $(c \rightarrow a \times b) =_c (c \rightarrow a) \times (c \rightarrow b)$ because my teacher told me so.

I think that I have to show the relation "$\leqslant$" first and then "$\geqslant$" by finding an injective function in both cases. For the latter I'm thinking that for every $(f_1 f_2) \in (c \rightarrow a)$ x $(c \rightarrow b)$ let $f: c \rightarrow a$ x $b$ be defined as $f(x) = (f_1(x), f_2(x))$ which gives the injective function $(f_1 f_2) \rightarrow f$ but I don't know how to verify. For "$\leqslant$" I tried to do it the other way around but it makes no sense..