The following algorithm give a correct answer 488

+_65_
5^1 5^1 3
Explain why the algorithm works

To explain why the algorithm works, let's break it down step by step.

First, the algorithm adds the numbers 488 and 65 to get a partial sum:

488
+ 65
------
10^1 5^1 3

The partial sum is 553.

Next, the algorithm raises 5 to the power of 1, which gives 5.

488
+ 65
------
5^1 5^1 3

Then, the algorithm adds the partial sum (553) and the result of the power operation (5) to get the final sum:

5^1 5^1 3
+ 553
------
5^2 5^1 3

The final sum is 553 + 5^1 = 553 + 5 = 558.

The algorithm works because each step operates independently and accurately performs the intended arithmetic operation. By breaking down the addition into smaller operations and combining the results, the algorithm correctly computes the final answer, which is 558.

Note: In this explanation, the notation "10^1" represents the decimal digit 1 followed by a zero.