Terry was asked to evaluate 2^7 . He multiplied 2 times 7 and got the answer 14. Explain why Terry’s answer is incorrect. Then, evaluate 2^7 .(4 points)

Answer 1

Terry's answer is incorrect because he misunderstood the concept of exponentiation. When evaluating \( 2^7 \), it means multiplying the base (which is 2) by itself a total of 7 times, not multiplying the base by the exponent. So, \( 2^7 \) is calculated as:

\[ 2^7 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \]

To evaluate \( 2^7 \):

1. Start with 2: \[ 2 \]
2. Multiply the first two 2's: \[ 2 \times 2 = 4 \]
3. Multiply the result by the next 2: \[ 4 \times 2 = 8 \]
4. Continue multiplying by 2: \[ 8 \times 2 = 16 \]
5. Multiply again: \[ 16 \times 2 = 32 \]
6. Multiply again: \[ 32 \times 2 = 64 \]
7. Finally, multiply one last time: \[ 64 \times 2 = 128 \]

Thus, \( 2^7 = 128 \).