To simplify the quotient (4^( 400)) / ( 5), we can break it down step by step.

First, let's simplify 4^( 400). Since 400 = 20, we have 4^( 400) = 4^20.

Next, let's simplify 5. Since the square root of 5 cannot be simplified further, we keep it as is.

Now, the quotient becomes (4^20) / ( 5).

To simplify this expression, we can rewrite 4^20 as (2^2)^20 = 2^(2*20) = 2^40.

Therefore, the simplified form of the quotient is (2^40) / ( 5).