Write the exponent of 3 in the prime factorization of 144.

Answer

To find the exponent of 3 in the prime factorization of 144, we will follow these steps:

### Step 1: Prime Factorization of 144
We start by dividing 144 by the smallest prime number, which is 2.

144 ÷ 2 = 72
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

Now, we have divided 144 down to 1 using prime numbers.

### Step 2: Write the Prime Factors
From the divisions, we can write the prime factors of 144:

- We divided by 2 four times: \(2 \times 2 \times 2 \times 2\) or \(2^4\)
- We divided by 3 two times: \(3 \times 3\) or \(3^2\)

Thus, the prime factorization of 144 is:
\[ 144 = 2^4 \times 3^2 \]

### Step 3: Identify the Exponent of 3
In the prime factorization \(2^4 \times 3^2\), we see that the exponent of 3 is 2.

### Final Answer
The exponent of 3 in the prime factorization of 144 is **2**.

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