Question

2 to the 12th power = 4,096. How many other whole numbers can you raise to a power to get 4,096! Explain or show your reasoning.

Answer 1

Other whole numbers that can be raised to a power to get 4,096 are 4, 8, 16 and 64

Explanation:

Given;

2¹² = 4096

Other whole numbers that can be raised to a power to get 4,096 are obtained as follows;

`if \ (a^x)^y = a^(xy)\\\\ (2^2)^6 = 4,096\\\\(4)^6 = 4,096\\\\Thus, \ the \ first \ whole \ number \ is \ 4\\\\(2^3)^4 = 4,096\\\\(8)^4 = 4,096\\\\Thus, \ the \ second \ whole \ number \ is \ 8\\\\(2^4)^3 = 4,096\\\\(16)^3 = 4,096\\\\Thus, \ the \ third \ whole \ number \ is \ 16\\\\(2^6)^2 = 4,096\\\\(64)^2 = 4,096\\\\Thus, \ the \ fourth \ whole \ number \ is \ 64`

Therefore, Other whole numbers that can be raised to a power to get 4,096 are 4, 8, 16 and 64