Question

Prove that:

a) 5^31–5^29 is divisible by 100.
The answer should be in this format: ____ * 100

b) 25^9+5^17 is divisible by 30.
The answer should be in this format: ____ * 30

c) 27^10–9^14 is divisible by 24.
The answer should be in this format: ____ * 24

Answer 1

6*5^27*100

Explanation:

Answer 2

(a) 5^31-5^29 = 5^29(5^2-1)

= 5^29(24)
= 5^29(6)(4)
=5^26(6)*[(5)(5)(4)]
=5^26(6)*100
(b) 25^9+5^17 = 5^18+5^17
=5^17(5+1)
=5^17(6)
=5^16[(5)(6)]
=5^16*30
(c) 27^10–9^14 = 3^30-3^28
=3^28(3^2 -1)
=3^28(8)
=3^27[(3)(8)]
=3^27*24