Algebra Practice Test

What is the exponent needed to obtain 16 from a base of 2?

1. 2

2. 4

3. 8

4. 3

The correct answer is: 4

To find the exponent needed to obtain 16 from a base of 2, we can express 16 as a power of 2. Specifically, 16 can be rewritten as \(2^4\). This means that when the base (2) is raised to the exponent (4), it equals 16: \[ 2^4 = 2 \times 2 \times 2 \times 2 = 16 \] Thus, the correct answer is that the exponent needed is 4. This illustrates the concept of exponents, where the base is multiplied by itself a certain number of times, dictated by the exponent itself. The other choices do not yield 16 when 2 is raised to those powers: - 2 raised to the power of 2 equals 4. - 2 raised to the power of 3 equals 8. - 2 raised to the power of 8 equals 256. This further confirms that the only exponent that correctly results in 16 is 4.