10. \( (8-\sqrt{-16})(3+\sqrt{-81}) \)

To solve the expression \( (8-\sqrt{-16})(3+\sqrt{-81}) \), we first simplify the square roots of the negative numbers. Starting with \(\sqrt{-16}\), we can rewrite it as: \[ \sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i \] Now, for \(\sqrt{-81}\): \[ \sqrt{-81} = \sqrt{81} \cdot \sqrt{-1} = 9i \] Now substituting back into the expression, we have: \[ (8 - 4i)(3 + 9i) \] Next, we can use the distributive property (also known as the FOIL method for binomials): \[ = 8 \cdot 3 + 8 \cdot 9i - 4i \cdot 3 - 4i \cdot 9i \] \[ = 24 + 72i - 12i - 36i^2 \] Here, recall that \(i^2 = -1\): \[ = 24 + 72i - 12i + 36 \] \[ = (24 + 36) + (72i - 12i) \] \[ = 60 + 60i \] Thus, the final simplified result of the expression \( (8-\sqrt{-16})(3+\sqrt{-81}) \) is: \[ \boxed{60 + 60i} \]