Dragon Ball, DB Z, DB GT/How much power can you increase from training in the ROSAT?
We know Goku was around 3,000,000 is base form when he came back to earth. How much did Goku increase his base form when training in the ROSAt and how did Goku increase training in the Other World
ANSWER: It's hard to say for certain just how much stronger he managed to get between his return to Earth following the fight with Freeza to the end of the Buu Saga, but we know for certain that he never made it above the 150,000,000 battle power of his Super Saiya-jin form. This is established in Battle of the Gods by North Kaiou confirming that Goku (even at that point) wouldn't be strong enough to defeat Freeza in his base form.
Given the relative progression that one could estimate from the established increases seen, we know that #17 is well over twice as powerful as Ssj Goku (Ssj Mirai Gohan was established to be at least as strong as Ssj Goku on Namek, and #17 was established to be well over twice as strong as Gohan was).
In turn, Cell in his first form was stronger than #17, and well over twice as strong as him in his second form.
This would put Cell's second form at potentially 5-6 times as strong as Ssj Goku.
Vegeta, in his Super Saiya-jin Grade 2 form, was likely 1.5x stronger than Cell's second form, and it's established that Full Power Super Saiya-jin Goku was over twice as powerful as Ssj Grade 2 Vegeta. This would put FpSsj Goku at possibly 20 times stronger than Ssj Goku in the Freeza Saga, or potentially 3,000,000,000, and his base form at 60,000,000.
Since Gohan was stronger than Goku at this time, but not necessarily by a staggering degree, his Ssj might have been around 4,000,000,000, or a base of 80,000,000, in turn putting his Ssj2 battle power to 8,000,000,000.
Goku, during the Buu Saga, was established to be stronger than Gohan was during the fight with Cell, so his Ssj2 battle power might have been around 10,000,000,000, which would put his base at about 100,000,000.
These numbers are subjective and not something that I can say are 100% accurate (since those comparisons in strength for the Cell Saga aren't stated, just educated guesses), but I would say they're definitely within the ballpark.
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QUESTION: Good analysis, but the problem is that is since the potara fusion is something multiplication 100,000,000 x 100,000,000
That means Super Boohan has to be around Vegetto's base. I don't know how Super Boo can even get that strong because of Kid Boo being around Ssj 3 Goku level.
Also how can we determine the power of South Kai and Grand Kai?
Well, the thing is with the Potara fusion is that it's not expressly stated that it is strictly multiplying their battle powers together. The SEG eludes to that a bit, but doesn't actually say that it is a cut and dry A x B = C sort of thing, just that the increase is so powerful, that it's like multiplication, which in turn could simply mean that it's not adding their battle powers together.
Likewise, we can infer that, since it's established that Gotenks and Gogeta are many times stronger than Goten/Trunks and Goku/Vegeta are (many times is mentioned for Gotenks, and dozens of times for Gogeta), then it can be inferred reasonably that Vegetto would be far higher than that, potentially hundreds of times stronger than Goku and Vegeta are.
Unfortunately with South and Dai Kaioushin, there's no true feats you can go on to get an accurate assessment of their strength. We know that Dai Kaioushin isn't as strong as South because South is established as the strongest, and if we go by what we see from how the other Buus act, South Kaioushin may have been stronger than Pure Buu given that Buu absorbed him (we've seen that, outside of with Dabura, Buu only absorbs others or uses his Henki Beam if his adversaries are stronger than he is and he needs it for a tactical advantage).