Use calculator to the minimum.
Under Logical Deduction, these Daunting Relations will quickly melt away to reveal the constituent digits.
All three sets show beautiful symmetric Relations with first and second part of strings with powers on other side.
A, B, C, D, E, F, G, H are single digits..can vary from 0 to 9.
All other letter combinations are Concatenated Numbers. Leading zeroes allowed in the numbers for symmetry sake.
$ABCC$ = $AB^B$ + $CC^B$
$DDCC$ = $DD^B$ + $CC^B$
$EAEAEE$ = $EAE^B$ + $AEE^B$
$FFEAEE$ = $FFE^B$ + $AEE^B$
$EGDDBCGC$ = $EGDD^B$ + $BCGC^B$
$FHABBCGC$ = $FHAB^B$ + $BCGC^B$
Further another relationship exists
$EGDD$ + $FHAB$ = $AE*(EAE+FAE)$ = $(AB+DD)*AE^B$