How do I find the sum of prime factors of $(1750 + 1225)^{1229}$? The number is: $(1750 + 1225)^{1229}$
My professor did this example in class, but I didn't really understand this. Please help.
Thanks.

Assuming, given the lack of clarity, that you need to find the sum of distinct prime factors (disregarding multiplicity of any given prime factor), find the prime factors of the sum $$1750 + 1225 = 2975$$
$$(1750 + 1225)^{1229} = (2975)^{1229}  = (5^2 \cdot 7 \cdot 17)^{1229}= \left(5^2\right)^{1229}\cdot (7)^{1229}\cdot (17)^{1229}$$
Now you need to determine whether you need to 


*

*sum $2\cdot 1229$ factors of 5, and $1229$ factors of $7$, and $1229$ factors of $17$

*or simply sum the distinct prime factors $5$ and $7$ and $17$: In the latter
case, your sum will be $5 + 7 + 17 = 29$.
Either way, you'll have your result.
