How to write 49 as a power? How to write 400 as a power? How to write 4096 as a power?

See the following examples.

Problem: Write 49 as a power of 2

Solution:

49 = 7 * 7 = 7^{2}

Problem: Write 400 as a power of 2

Solution:

400 = 4 * 100 =

(2 * 2) * (10 * 10) =

2^{2} * 10^{2} =

(2 * 10)^{2} = 20^{2}

(2 * 2) * (10 * 10) =

2

(2 * 10)

Problem: Write 4096 as a power of 12

Solution:

4096 = 4 * 1024 =

4 * 4 * 256 =

4 * 4 * 4 * 64 =

4 * 4 * 4 * 8 * 8 =

2^{2} * 2^{2} * 2^{2} * 2^{3} * 2^{3} =

=2^{2 + 2 + 2 + 3 + 3} =

2^{12}

4 * 4 * 256 =

4 * 4 * 4 * 64 =

4 * 4 * 4 * 8 * 8 =

2

=2

2