Question

1. Write an expression with an exponent that represents 256 with 2 as the base. Show your work.

Answer 1

Using the prime factorization, we have:

256 I 2 (Dividing by 2 as the number is even)

128 I 2 (Dividing by 2 as the number is even)

64 I 2 (Dividing by 2 as the number is even)

32 I 2 (Dividing by 2 as the number is even)

16 I 2 (Dividing by 2 as the number is even)

8 I 2 (Dividing by 2 as the number is even)

4 I 2 (Dividing by 2 as the number is even)

2 I 2 (Dividing by 2 as the number is even)

1

We see that we can rewrite 256 as 2^8