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Question 52

The sum of digits of the number $$(625)^{65} \times (128)^{36}$$ is

Correct Answer: 25

Solution

$$625=5^4$$ 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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