Express the prime factorization of 144 as a product of prime factors by filling in the missing exponents after the caret.(1 point)

Question

2^
• 3^
= 144
Remaining Attempts : 3

Answer 1

To express the prime factorization of 144, we can break it down as follows:

144 can be divided by 2:

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

Counting the number of times we divided by each prime factor, we get:

• 2 appears 4 times, and
• 3 appears 2 times.

Thus, the prime factorization of 144 is:

\( 2^4 \cdot 3^2 = 144 \)

So, the answer is:

\( 2^4 \cdot 3^2 = 144 \)