a) \({\left( { - 7} \right)^3}{.2^4} = \left( { - 7} \right).\left( { - 7} \right).\left( { - 7} \right).2.2.2.2\)
\(= - 343.16 = - 5488\)
b)
\(\begin{array}{l}
{5^4}.{\left( { - 4} \right)^2}\\
= 5.5.5.5.\left( { - 4} \right).\left( { - 4} \right)\\
= 25.25.\left( { - 4} \right).\left( { - 4} \right)\\
= 25.\left( { - 4} \right).25.\left( { - 4} \right)\\
= - 100.\left( { - 100} \right)\\
= 10000
\end{array}\)