Express the prime factorization of 144 as a product of prime factors by filling in the missing exponents after the caret

Question

2^_ times 3^_ =144

Answer 1

To express the prime factorization of 144, we first find its prime factors:

1. Start by dividing 144 by 2:

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

2. Now, divide by 3:

   • 9 ÷ 3 = 3
   • 3 ÷ 3 = 1

Putting this together, we can express 144 as a product of its prime factors:

\[ 144 = 2^4 \times 3^2 \]

So, filling in the missing exponents:

\[ 2^4 \times 3^2 = 144 \]

Thus, the exponents are 4 for 2 and 2 for 3:

Answer: 2^4 times 3^2 = 144