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

Question

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