Question

For the following numbers, decide whether each number is less than or greater than one million without using a calculator. Explain.

1. 3^6 (3 to the 6th)
2. 9^5 (9 to the 5th)
3. 12^6 (12 to the 6th)

Answer 1

Focus on one million first: 10^6 = 1,000,000.

Then it becomes obvious that 3^6 is less than one million, because the base 3 is smaller than the base 10 in 10^6.

Next: 9^5: Both the base (9) and the exponent (5) are smaller than the base (10) and the exponent (6) of 10^6. What is your conclusion?