Find the exponent of 80 in 200!.

Explanation

To find the exponent of 80 in \(200!\), we first need to express 80 in terms of its prime factors.

### Step 1: Prime Factorization of 80
We can factor 80 as follows:
\[ 80 = 8 \times 10 = 2^3 \times (2 \times 5) = 2^4 \times 5^1 \]
Thus, the prime factorization of 80 is:
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