numpy.power() breaks down - numpy

Question

I am plotting a few exponential functions with different bases against the factorial function.
When going up to x=15 everything looks nice and we have a tight race:
However when going up to x=50, all the exponential functions seem to be upset that the factorial won the race and they all break down:
I doubt that it would be an overflow as I use dtype=np.longlong and the function values only reach about 10^60. Moreover, the factorial function is still doing fine.
Any idea of what could be going on?
Here is the code:
import numpy as np
import matplotlib.pyplot as plt
def compare_exponential_factorial(bases, x):
xs = np.arange(0, x, dtype=np.longlong)
fact = []
for x in xs:
fact.append(np.math.factorial(x))
fig, ax = plt.subplots(1,1, figsize=(8,6))
ax.semilogy(xs, fact, label="$f_1 = x!$", color="r")
exps = []
for i, b in enumerate(bases):
exp = np.power(b, xs, dtype=np.longlong)
exps.append(exp)
ax.plot(xs, exp, label=f"$f_{i + 2} = {b}^x$", color="b", alpha=(i + 1) / len(bases))
ax.set_xlabel("x")
ax.set_title("Epic race between Exponentials and Factorial functions", fontsize=14)
ax.legend(loc='best')
plt.show()
if __name__ == "__main__":
compare_exponential_factorial(bases=np.array([2, 3, 4, 5, 8, 10, 15], dtype=np.longlong), x=50)