Question
Express the prime
factorization of 54 as a
product of prime numbers with
exponents.
factorization of 54 as a
product of prime numbers with
exponents.
Answers
GPT-4o mini
To express the prime factorization of 54 as a product of prime numbers with exponents, we first need to factor 54 into its prime components.
1. Divide 54 by the smallest prime number, which is 2:
\[
54 \div 2 = 27
\]
So, we have one factor of 2.
2. Next, we factor 27. The smallest prime factor of 27 is 3:
\[
27 \div 3 = 9
\]
3. Continuing to factor 9, we again divide by 3:
\[
9 \div 3 = 3
\]
4. Finally, we have:
\[
3 \div 3 = 1
\]
Now, we can express 54 as a product of its prime factors:
\[
54 = 2^1 \times 3^3
\]
Thus, the prime factorization of 54, expressed as a product of prime numbers with exponents, is:
\[
2^1 \times 3^3
\]
1. Divide 54 by the smallest prime number, which is 2:
\[
54 \div 2 = 27
\]
So, we have one factor of 2.
2. Next, we factor 27. The smallest prime factor of 27 is 3:
\[
27 \div 3 = 9
\]
3. Continuing to factor 9, we again divide by 3:
\[
9 \div 3 = 3
\]
4. Finally, we have:
\[
3 \div 3 = 1
\]
Now, we can express 54 as a product of its prime factors:
\[
54 = 2^1 \times 3^3
\]
Thus, the prime factorization of 54, expressed as a product of prime numbers with exponents, is:
\[
2^1 \times 3^3
\]