Question

Express the prime
factorization of 128 as a
product of prime numbers with
exponents.

Answer 1

The prime factorization of 128 can be determined by repeatedly dividing by the smallest prime number, which is 2.

Here's how it's done:

1. Divide 128 by 2:
\(128 ÷ 2 = 64\)

2. Divide 64 by 2:
\(64 ÷ 2 = 32\)

3. Divide 32 by 2:
\(32 ÷ 2 = 16\)

4. Divide 16 by 2:
\(16 ÷ 2 = 8\)

5. Divide 8 by 2:
\(8 ÷ 2 = 4\)

6. Divide 4 by 2:
\(4 ÷ 2 = 2\)

7. Divide 2 by 2:
\(2 ÷ 2 = 1\)

Now, we have divided 128 by 2 a total of 7 times, so we can express the prime factorization of 128 as:

\[
128 = 2^7
\]

Thus, the prime factorization of 128 is \(2^7\).