a. \( \left(-24: 3-7^{0}\right) \cdot 2+\sqrt{7} \cdot \sqrt{28}+\left(12-2^{4}\right)^{3}= \)
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To simplify the expression step by step, let's proceed. First, simplify the first part: \[ -24: 3 - 7^{0} = -24 / 3 - 1 = -8 - 1 = -9 \] Now multiply by 2: \[ -9 \cdot 2 = -18 \] Next, simplify \(\sqrt{7} \cdot \sqrt{28}\): \[ \sqrt{7} \cdot \sqrt{28} = \sqrt{7 \cdot 28} = \sqrt{196} = 14 \] Now, simplify the last part: \[ 12 - 2^{4} = 12 - 16 = -4 \] Now raise it to the third power: \[ (-4)^{3} = -64 \] Now combine everything together: \[ -18 + 14 - 64 = -68 \] Thus, the final answer is: \[ \boxed{-68} \]