Question

Express the prime factorization of 54 as a product of prime numbers with exponents.(1 point)
a
Remaining Attempts : 2

Answer 1

To find the prime factorization of 54, we can break it down step by step:

1. 54 is an even number, so we can start by dividing it by 2:
\[
54 \div 2 = 27
\]

2. Next, we factor 27. Since 27 is not even, we try the next smallest prime number, which is 3:
\[
27 \div 3 = 9
\]

3. We continue factoring 9, which is also divisible by 3:
\[
9 \div 3 = 3
\]

4. Finally, we factor 3, which is already a prime number:
\[
3 \div 3 = 1
\]

Now we can compile these factors together:
- We have used the prime factor 2 once.
- We have used the prime factor 3 three times.

Thus, the prime factorization of 54 is:
\[
54 = 2^1 \times 3^3
\]

So, the answer is:
\[
\boxed{2^1 \times 3^3}
\]