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The sum of digits of the number $$(625)^{65} \times (128)^{36}$$ is
Correct Answer: 25
$$625=5^4$$ and $$128=2^7$$
So, $$(625)^{65},(128)^{36}=5^{260},2^{252}=(2^{252}5^{252})\cdot5^8=10^{252}\cdot5^8$$
Thus, the number equals $$5^8$$ followed by 252 zeros. Now (5^8=390625), and the sum of the digits of (390625) is
$$ 3+9+0+6+2+5=25.$$
Zeros add nothing, so the required sum of digits is 25.
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