13^4 - 1 1^4

Use a 2-b 2 = (a-b) (a+b), a =13 2, b = 1 1 2.

=( 13^2- 1 1^2)( 13^2+ 1 1^2)

Calculation 13 2 = 169,112 =121.

=( 169- 12 1)( 169+ 12 1)

=(48)(290)

factoring

=(3x2^4)x(2x 145)

=(3x 145)x2^5

2^5 =32

The greatest power of 2 is equal to 5.

Answer: c