Question
Express 80 as a product of prime numbers with exponents. Responses 24 × 5 24 × 5 - no response given 23 × 10 23 × 10 - no response given 25 × 5 25 × 5 - no response given 23 × 5
Answers
Answered by
GPT-4o mini
To express \( 80 \) as a product of prime numbers with exponents, we first need to factor \( 80 \).
1. Start by dividing \( 80 \) by the smallest prime number, \( 2 \):
\[
80 \div 2 = 40
\]
2. Continue dividing by \( 2 \):
\[
40 \div 2 = 20
\]
3. Continue:
\[
20 \div 2 = 10
\]
4. Continue:
\[
10 \div 2 = 5
\]
5. Finally, \( 5 \) is a prime number.
Now we can list the factors:
- We divided \( 80 \) by \( 2 \) four times, so \( 2^4 \).
- We have one \( 5 \).
Putting it all together:
\[
80 = 2^4 \times 5^1
\]
Thus, the prime factorization of \( 80 \) is:
\[
80 = 2^4 \times 5^1
\]
1. Start by dividing \( 80 \) by the smallest prime number, \( 2 \):
\[
80 \div 2 = 40
\]
2. Continue dividing by \( 2 \):
\[
40 \div 2 = 20
\]
3. Continue:
\[
20 \div 2 = 10
\]
4. Continue:
\[
10 \div 2 = 5
\]
5. Finally, \( 5 \) is a prime number.
Now we can list the factors:
- We divided \( 80 \) by \( 2 \) four times, so \( 2^4 \).
- We have one \( 5 \).
Putting it all together:
\[
80 = 2^4 \times 5^1
\]
Thus, the prime factorization of \( 80 \) is:
\[
80 = 2^4 \times 5^1
\]