First, let's simplify the expression inside the square root:

[tex] \sqrt[4]{2 ^{7} } = \sqrt[4]{2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2} = \sqrt[4]{128} = 2 [/tex]

Now, we can rewrite the entire expression as:

[tex] \sqrt[4]{2 ^{7} } \times {10}^{3} = 2 \times 10^{3} = 2 \times 1000 = 2000 [/tex]

Therefore, the value of the expression is 2000.