What exponent should you raise the base of 2 to reach the value of 64?

• A. 4
• B. 5
• C. 6
• D. 7

Answer: (C)

To determine the correct exponent to raise the base of 2 in order to reach the value of 64, we can start by expressing 64 as a power of 2. Recognizing that 64 can be broken down through successive divisions by 2 aids in this calculation:

• 64 divided by 2 gives 32

• 32 divided by 2 gives 16

• 16 divided by 2 gives 8

• 8 divided by 2 gives 4

• 4 divided by 2 gives 2

• 2 divided by 2 gives 1

Counting these steps reveals that 64 can be expressed as (2^6) since it takes six divisions by 2 to reach 1. Therefore, the exponent that 2 must be raised to in order to equal 64 is indeed 6.

The reasoning behind the other options does not align with the calculation of 64 as a power of 2. For example, raising 2 to the fourth power gives 16, and raising it to the fifth power gives 32, both of which do not equate to 64. Meanwhile, raising 2 to the seventh power results in 128, which overshoots