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The size of powers grows exponentially, so before computing it's worth checking whether it'd be possible to accommodate the result in memory. As for your specific powers p**e - 1, you can compute first f**(p**e) by iterative raising to power p, and then divide the result by f:

f = X**7 + Y**5
g = f
for e in range(1, 10):
    g **= p
    print( e, g//f )

However, be prepared that this computation will die after first few values due to enormous and ever growing size of the result.