Prove that the value of the expression 12^5+12^4 is divisible by 13.
_____*13
To prove that the value of the expression 12^5 + 12^4 is divisible by 13, we can simplify the expression and use the fact that if a number is divisible by 13, then its remainder when divided by 13 is 0.
Step 1: Calculate 12^5.
12^5 = 12 * 12 * 12 * 12 * 12 = 248,832
Step 2: Calculate 12^4.
12^4 = 12 * 12 * 12 * 12 = 20,736
Step 3: Add the two values together.
12^5 + 12^4 = 248,832 + 20,736 = 269,568
Step 4: Check if the sum is divisible by 13.
269,568 ÷ 13 = 20,736 remainder 0
Since the remainder is 0 when dividing 269,568 by 13, we can conclude that the value of the expression 12^5 + 12^4 is divisible by 13.
To prove that the value of the expression 12^5 + 12^4 is divisible by 13, we can use modular arithmetic.
Modular arithmetic involves performing operations with remainders. In this case, we would perform the given operations and consider the remainder when divided by 13. A number is divisible by 13 if and only if its remainder is 0 when divided by 13.
Let's calculate the values of 12^5 and 12^4 separately:
12^5 = 248,832
12^4 = 20,736
Now, let's add these two values:
248,832 + 20,736 = 269,568
To determine if 269,568 is divisible by 13, we divide it by 13 and check the remainder:
269,568 ÷ 13 = 20,736
The remainder is 0, meaning that 269,568 is divisible by 13. Therefore, the value of the expression 12^5 + 12^4 is divisible by 13.