Question

Prove that:
7^16+7^14 is divisible by 50.

Answer 1

One trick you could do is factor out the GCF 7^14 and note how 50 is one of the factors left over

7^16 + 7^14 = 7^14(7^2 + 1)

7^16 + 7^14 = 7^14(49 + 1)

7^16 + 7^14 = 7^14*50

Since 50 is a factor of the original numeric expression, this means the original expression is divisible by 50.

Answer 2

`7^(16)+7^(14)=7^(14)(7^2+1)=7^(14)\cdot 50`