Question

Determine the exponent of the prime factor 3 when expressing the prime factorization of 54.(1 point)
Responses

3
3

1
1

2
2

0

Answer 1

To determine the exponent of the prime factor 3 in the prime factorization of 54, we first need to find the prime factorization of 54.

1. Start with the number 54:
- 54 is even, so we can divide it by 2:
\[ 54 \div 2 = 27 \]
- Now, we have 2 as a prime factor and are left with 27.

2. Next, we factor 27:
- 27 can be divided by 3:
\[ 27 \div 3 = 9 \]
- So, we have one 3 as a factor.

3. Continuing with factoring 9:
- 9 can also be divided by 3:
\[ 9 \div 3 = 3 \]
- So, we have another 3.

4. Finally, we factor the last 3:
- 3 can be divided by 3:
\[ 3 \div 3 = 1 \]
- So, we have one more 3.

Putting this all together, the prime factorization of 54 is:
\[ 54 = 2^1 \times 3^3 \]

Now, we can see that the exponent of the prime factor 3 in the prime factorization of 54 is **3**.

Thus, the answer is:
**3**