When ma*m b = m(a+b), why are a and b added instead of multiplied?

When like terms with exponents are multiplied, the number of times the term is multiplied by itself is increased by the additional number of times indicated by the second exponent. Therefore, the product is found by adding the exponents together.

For example, m³ x m⁴ = m⁷, because m³ is equivalent to (m x m x m), and m⁴ is equivalent to (m x m x m x m). The product of these terms is m⁷, because m is multiplied by m a total of seven times. On the other hand, if m³ is raised to the fourth power, the answer is found by multiplying the exponents, so (m³)⁴ = m¹².