Which of the following has the highest value?
20242023
Which of the following has the highest value?
- A.
10 power 11
- B.
12 power 9
- C.
5 power 5
- D.
11 power 10
Attempted by 106 students.
Show answer & explanation
Correct answer: A
To determine which of these expressions has the highest value, we can evaluate each one by approximating their magnitudes:
Step-by-Step Evaluation
Option A: 10 raised to the power of 11 This is equal to 1 followed by 11 zeros. Value: 100,000,000,000 (100 billion).
Option B: 12 raised to the power of 9 We can estimate this by noting that 12 is close to 10. 10 raised to the power of 9 is 1,000,000,000 (1 billion). 12^9 is larger than 1 billion, but significantly smaller than 100 billion. Value: ~515,978,035.
Option C: 5 raised to the power of 5 Value: 5 * 5 * 5 * 5 * 5 = 3,125. This is clearly the smallest value among all options.
Option D: 11 raised to the power of 10 We can estimate this by noting that 11 raised to the power of 10 is slightly larger than 10 raised to the power of 10. 10 raised to the power of 10 is 10,000,000,000 (10 billion). Value: ~25,937,424,601 (approximately 25.9 billion).
Comparative Summary
By comparing the approximate values:
Option A: 100 billion
Option D: 25.9 billion
Option B: 0.5 billion
Option C: 0.000003 billion