Q20
The sum of digits of the number \( ( 625 ) ^ { 65 } \times ( 128 ) ^ { 36 } \), is
Answer: 25
Key idea: Pair 2s with 5s to make powers of 10, which only add trailing zeros.
\(625^{65} = 5^{260}\) and \(128^{36} = 2^{252}\). So
\[5^{260} \times 2^{252} = 10^{252} \times 5^{8} = 390625 \times 10^{252}.\]The trailing zeros add nothing, so the digit sum is \(3 + 9 + 0 + 6 + 2 + 5 = 25\).
Hence, the answer is 25.