If a person has the genotype aabbccddeeffgg, then each of their gametes (eggs or sperm) will receive one allele from each of the 7 gene pairs. The total number of possible gametes is then the product of the number of possible alleles for each gene pair, which is 2 for each pair since each person has two copies of each gene.
Therefore, the total number of genetically different eggs that can be formed by a person with the genotype aabbccddeeffgg is:
2^7 = 128
So there are 128 genetically different eggs that could be formed by a person with the genotype aabbccddeeffgg.