Question

3^20 = 3,486,784,401. How many other whole numbers can you raise to a power

and get 3,486,784, 401? Explain or show your reasoning.

Answer 1

Two more whole numbers 9 and 81

Explanation:

`3^(20) = 3,486,784,401 \\ \\ ( {3}^(2) )^(10) = 3,486,784,401 \\ \\ \huge \red{ \boxed{{9}^(10) = 3,486,784,401}} \\ \\ ( {9}^(2) )^(5) = 3,486,784,401 \\ \\ \huge \red{ \boxed{{81}^(5) = 3,486,784,401 }}\\ \\`

So, two more whole numbers 9 and 81 can be raised to a power to get 3,486,784, 401.