Final answer:
To find the three-digit number abc in the equation a ab abc = bcb, substitute the value of c as 0 and test different values for a and b until a combination is found that satisfies the equation. The number abc is then 930.
Step-by-step explanation:
To find the three-digit number abc in the equation a ab abc = bcb, we can use the information given about cubing of exponentials. In the equation, each of the letters a, b, and c represents a different digit.
Since the number abc is a three-digit number, we know that a and b cannot be equal to zero. Therefore, the only possible digit for c is 0.
To determine the values of a and b, we can substitute the value of c as 0 into the equation. This gives us a ab ab0 = b0b. Simplifying further, we get a ab0 = bb.
Since each letter represents a different digit, we can try different values for a and b until we find a combination that satisfies the equation. After testing a few values, we find that a = 9 and b = 3 work. Therefore, the three-digit number abc is 930.