Question

What is the prime factorization of 81?
A.
34
B.
32 · 9
C.
9 · 3
D.
3 · 27

Answer 1

To find the prime factorization of 81, we can break it down as follows:

1. \( 81 = 9 \times 9 \)
2. Then, since \( 9 = 3 \times 3 \), we can rewrite this as:
\[
81 = (3 \times 3) \times (3 \times 3) = 3^2 \times 3^2 = 3^4
\]

So, the prime factorization of 81 is \( 3^4 \).

Now, let's check which of the options provided match the prime factorization of 81:

- **Option A:** 34 (not related)
- **Option B:** \( 32 \cdot 9 \) (not correct as \( 32 = 2^5 \) and is not a prime factor of 81)
- **Option C:** \( 9 \cdot 3 = (3^2) \cdot 3 = 3^3 \) (not correct)
- **Option D:** \( 3 \cdot 27 = 3 \cdot (3^3) = 3^4 \) (correct)

The correct answer is **D: 3 · 27**.