hwgramm

Why does this always work when one of the terms is a square?

Example: 7² + 7³ = 392

Rule: One of the terms must be a square (raised to the power of 2) and the bases must be the same.

Process: Subtract two from the term with the greater power and add one to the result then multiply this sum by the square of the same base. In our example 7³ becomes 7¹ and we add 1 to it.

7²(1+7¹) = 49(8) = 392

Let's try another with the power of 9: 7^2 + 7^9 : 9-2 = 7 : 7^2(1+7^7) = 49(1+823543) = 40353656

As long as one of the terms is a square and the bases are the same, we are able to add the exponents in this way. Why does this work? Are there any other methods of adding exponents of the same base?

???

http://antiques.about.com/gi/dynamic/offsite.htm?z...

Some threads have off topic replies (runaway discussion) - I would like to move the replies to a new topic that is in line with the subject matter. Is this possible? How can it be done?