Question

Prove that the value of the expression 12^5+12^4 is divisible by 13.
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Answer 1

Explanation:

To prove that the expression 12^5 + 12^4 is divisible by 13, we need to show that the remainder when this expression is divided by 13 is zero.

We can start by simplifying the expression using the laws of exponents:

12^5 + 12^4 = 12^4 × 12 + 12^4 = 12^4 × (12 + 1) = 12^4 × 13

Now we can see that 12^4 × 13 is a multiple of 13, which means that it is divisible by 13 with no remainder. Therefore, the original expression 12^5 + 12^4 is also divisible by 13, since it is equal to 12^4 × 13.

This proves that the value of the expression 12^5 + 12^4 is divisible by 13.