Hopefully everyone has heard of the Super Saiyan gene theory, if you haven't let me give you a quick explanation. Basically what the theory entails is that the reason why both Goten and Trunks were able to achieve SSJ with zero effort and training compared to Goku, who had to undergo a lot of stress and the death of his friends, Vegeta, who had to undergo rigorous, and Gohan who had to experience the death of all his friends, is because after becoming SSJ for the first time, Goku and Vegeta unlocked the "Super Saiyan Gene" and passed it down to both Goten and Trunks. Since Gohan was conceived before Goku became SSJ, he didn't inherit the gene and had to achieve SSJ the hard way.
The TheoryNow I believe that Pan somehow inherited Gohan's mystic abilities in a similar fashion to the SSJ gene theory. This would explain her ability to charge up ki, her ability to breathe in space, and her great show of strength. Goten and Trunks were just learning to walk at Pans age, which is still impressive for babies, but not as impressive as Pan. This would also explain why even though she's only 1/4 saiyan, she's stronger than 1/2 saiyan Goten and Trunks were.
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The Theory