What is the product of A to the M power and A to the N power, when M and N are positive integers?

The product of (A) raised to the power (M) and (A) raised to the power (N) can be expressed with the laws of exponents. According to these laws, when multiplying two expressions with the same base, you add the exponents.

Therefore, when you multiply (A^M) and (A^N), you can rewrite it as:

[

A^M \times A^N = A^{M + N}

]

This shows that the result of the operation is (A) raised to the sum of the exponents (M) and (N). Consequently, this reinforces the idea that for any positive integers (M) and (N), the product of (A^M) and (A^N) is indeed (A) raised to the power of (M + N).

This reasoning aligns perfectly with option A, which reflects the correct mathematical interpretation of the operation.