Which explanation best justifies why multiplying powers with the same base will mean that you can add the exponents, while dividing them will mean that you can subtract the exponents?

• A. Exponents count repeated factors. When multiplying, the factor lists combine, so the exponents can be added together like so: a^m × aⁿ = a^m+n. When dividing, the matching factors will cancel, so the exponents will subtract like so: a^m / aⁿ = a^m-n.
• B. Multiplication and division cannot be explained all together by using factors. Adding or subtracting exponents is just a coincidence with no real justification from repeated multiplication.
• C. Multiplication adds exponents because the exponents themselves are multiplied together. Division subtracts exponents because dividing them inverts the denominator before multiplying.
• D. Exponents represent logarithms. Multiplication adds the logs, and division subtracts the logs. This is the only correct justification.

Answer: (A)