Answer:
a) done in the previous question.
See below for b and c.
Step-by-step explanation:
(b) 27^4 - 9^5 + 3^9.
Change these terms to base 3:
= 3^(4*3) - 3^(2*5) + 3^9
= 3^12 - 3^10 + 3^9
= 3^9( 3^3 - 3 + 1))
= 25 * 3^9 so its divisible by 25.
c. 16^4–2^13–4^5
Change to base 2:
= 2^(4*4) - 2^13 - 2^(2*5)
= 2^16 - 2^13 - 2^10
= 2^10 (2^6 - 2^3 - 1)
= 2^10 ( 64 - 8 - 1)
= 55 * 2^10
= 11*5 *2^10 which is divisible by 11.
