First, let's simplify the expression.

[ \sqrt[4]{ 2^{12} } = 2^{12 \div 4} = 2^3 = 8 ]

Now, we can continue simplifying the expression:

[ \sqrt[4]{ 2^{12} } \times 5^{8} = 8 \times 5^{8} ]

[ = 8 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 ]

[ = 8 \times 390625 ]

[ = 3125000 ]

Therefore,

[ \sqrt[4]{ 2^{12} } \times 5^{8} = 3125000 ]