A certain program makes $176,000,840$ data memory accesses $($reads or writes$).$ Each memory access takes $128$ ns$.$ To improve performance, a proposal is made to use a data cache for the system with an access time of $10$ ns$.$ The cache has a hit ratio of $90\%.$

a$)(3)$ What is the total number of nano$-$seconds required to perform all $176,000,840$ data accesses if the cache operates in look$-$through mode?

b$)(3)$ What is the total number of nano$-$seconds required to perform all $176,000,840$ data accesses if instead the cache operates in look$-$aside mode?