Show the F1 and F2 progeny phenotypic and genotypic ratios of the following dihybrid cross involving unlinked purebred Mendelian traits (tall plants, long stems X dwarf plants, short stems) under the following conditions:

a. the alleles for tall plants and long stems are dominant
b. the alleles for height and stem length are each codominant
c. the allele specifiying plant height is epistatic to the allele specifying stem length

I wrote:
P generation= TTSS x ttss
F1 generation= TtSs
Therefore the F1 progeny are all tall with long stems. How do I write the genotypic and phenotypic ratios? Is it just 1 or is it 1:0 TtSs?

F1= TS, Ts, tS, ts x TS, Ts, tS, ts
I know the genotypic ratio of the F2 progeny is 1:2:2:1:4:2:1:2:1
(TTSS:TTSs:TtSS:TTss:TtSs:Ttss:ttSS:ttSs:ttss)
But the epistatic gene is confusing me on the phenotypic ratio. Does that mean that unless plant height = tt (recessive) the stem length will be long? I don't think I understand that. But if that's the case then the phenotypic ratio would be:
3:3:1:1:1
(Tall, long: medium long: dwarf long: dwarf medium: dwarf short)

Does that look right?

Yes, overall your understanding of the dihybrid cross and the genotypic ratios is correct. However, there are a few clarifications needed to determine the correct phenotypic ratios considering the different conditions mentioned in the question.

a. The alleles for tall plants and long stems are dominant:
In this case, when the alleles for tall plants (T) and long stems (S) are dominant, the F1 generation will be heterozygous for both traits (TtSs). Therefore, all the F1 progeny will be tall with long stems.

b. The alleles for height and stem length are codominant:
If the alleles for height (T) and stem length (S) are codominant, this means that in the F1 generation (TtSs), both traits will express themselves equally. This would result in a phenotypic ratio of 1:1 for tall with long stems and medium height with medium stems.

c. The allele specifying plant height is epistatic to the allele specifying stem length:
In this case, the allele specifying plant height (T) is epistatic to the allele specifying stem length (S). Epistasis refers to the interaction between different genes where one gene can mask or override the expression of another gene. If the allele for plant height is epistatic to stem length, it means that the presence of the recessive allele for plant height (tt) would result in the expression of the recessive trait for stem length, regardless of the other alleles present.

Based on this information, the correct phenotypic ratio for the F2 progeny would be as follows:

- Tall with long stems: 3
- Medium height with medium stems: 3
- Dwarf with long stems: 1
- Dwarf with medium stems: 1
- Dwarf with short stems: 1

Therefore, the phenotypic ratio would be 3:3:1:1:1 for tall with long stems, medium height with medium stems, dwarf with long stems, dwarf with medium stems, and dwarf with short stems, respectively.

It's important to note that the phenotypic ratios can vary depending on the specific conditions and genetic interactions mentioned in the question.