Express the prime factorization of 84 with exponents.(1 point)

Question

Responses

3 ⋅4⋅7
3 times 4 times 7

2 ⋅ 3 ⋅ 7
2 times 3 times 7

22 ⋅ 3 ⋅ 7
2 squared times 3 times 7

2 ⋅ 32 ⋅7

Answer 1

The prime factorization of 84 can be found by dividing it by the smallest prime numbers.

1. Start by dividing by 2:
   \( 84 ÷ 2 = 42 \)
   \( 84 = 2 × 42 \)

2. Divide 42 by 2 again:
   \( 42 ÷ 2 = 21 \)
   \( 84 = 2^2 × 21 \)

3. Now divide 21 by the next smallest prime number, which is 3:
   \( 21 ÷ 3 = 7 \)
   \( 84 = 2^2 × 3 × 7 \)

Thus, the complete prime factorization of 84 is:

\[ 2^2 × 3^1 × 7^1 \]

In exponent form, it is represented as \( 2^2 × 3 × 7 \).

Among the given responses, the correct answer expressed with exponents is:

22 ⋅ 3 ⋅ 7 (This represents \( 2^2 \cdot 3^1 \cdot 7^1 \))