Please explain how to multiply two exponential expressions

In the multiplication of exponential expressions, only exponents are added given that the expressions share the same base. If this is not the case, the expression remains the same or can be simplified. Hence, there are four possible scenarios:Case 1: A² x A³ = A⁽²⁺³⁾ = A⁵. Both expressions have the same base and are being multiplied, therefore we only add exponents.Case 2: (A⁴)² = A⁴ x A⁴ = A⁽⁴⁺⁴⁾ = A⁸. Where A⁴ x A⁴ is the expansion of (A⁴)².Case 3: A² x B⁵ = A²B⁵. Expression is unchanged as they do not share a common base.Case 4: A⁴ x B² = (A² x B) x (A² x B) = (A² x B)². Where (A² x B)² is the simplification of (A² x B) x (A² x B).