To simplify the expression \((8 \sqrt{10})(8 \sqrt{5})\), we can follow these steps:
1. Multiply the coefficients:
[tex]\[
8 \times 8 = 64
\][/tex]
2. Multiply the square roots:
[tex]\[
\sqrt{10} \times \sqrt{5} = \sqrt{10 \times 5} = \sqrt{50}
\][/tex]
3. Combine the results from steps 1 and 2:
[tex]\[
64 \times \sqrt{50}
\][/tex]
Therefore, an intermediate form of the expression is \(64 \sqrt{50}\).
Next, observe that \(\sqrt{50}\) can be further simplified:
[tex]\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2}
\][/tex]
Substitute this simplification back into the expression:
[tex]\[
64 \sqrt{50} = 64 \times 5 \sqrt{2} = 320 \sqrt{2}
\][/tex]
Thus, the simplified form of \((8 \sqrt{10})(8 \sqrt{5})\) is \(\boxed{320 \sqrt{2}}\).
So, the correct answer is:
[tex]\[
\boxed{D}
\][/tex]
