To express 80 as a product of prime numbers with exponents, we first need to perform the prime factorization of 80.
- Start with 80.
- Divide by 2 (the smallest prime number):
- \(80 \div 2 = 40\)
- Divide 40 by 2:
- \(40 \div 2 = 20\)
- Divide 20 by 2:
- \(20 \div 2 = 10\)
- Divide 10 by 2:
- \(10 \div 2 = 5\)
- Finally, 5 is a prime number.
Collecting all the factors, we have:
- \(80 = 2 \times 2 \times 2 \times 2 \times 5\)
In exponent form, this is represented as:
- \(80 = 2^4 \times 5^1\)
Thus, the prime factorization of 80 with exponents is:
\[ 80 = 2^4 \times 5^1 \]