STD_LOGIC_VECTOR multipication

The multiplication returns and unsigned, not a std_logic_Vector. So with your code, you need to write:

EXPx63_LTCHD <= std_logic_Vector( unsigned(EXP_LTCHD) * unsigned(COEFF) );

But why have you used std_logic_vector. Surely its better just to write:

constant COEFF : unsigned(5 downto 0) := x"3F";
signal EXPx63_LTCHD : unsigned(27 downto 0);
signal EXP_LTCHD:	unsigned(22 downto 0);
EXPx63_LTCHD <= EXP_LTCHD * COEFF;

Remember, ports do NOT have to be std_logic_Vector.