:18357252 For the record, the issue does appear to have been addressed in V10.0.1. The following yielded no problems for me:
powersMatrix = DiagonalMatrix[
{10^123, 10^152, 10^185, 10^220, 10^397, 10^449, 10^503, 10^563,
10^979, 10^1059, 10^1143, 10^1229, 10^1319, 10^1412}];
Do[
SeedRandom[k];
basicMatrix =
Table[Table[RandomInteger[{-99, 99}], {i, 1, 14}], {j, 1, 14}];
smallMatrix =
Table[Table[RandomInteger[{-999, 999}], {i, 1, 14}], {j, 1, 14}];
bigMatrix = basicMatrix.powersMatrix + smallMatrix;