Consider the following two statements:

Statement 1: 2^m x 3ⁿ = (2 + 3)^{m + n}, where m, n are positive integers.

Statement 2: If a is a rational number, and m, n are integers, then a^m.aⁿ = a^{m + n}

Which of the following is valid?

1. Both the Statements are true.

2. Both the Statements are false.

3. Statement 1 is true, and Statement 2 is false.

4. Statement 1 is false, and Statement 2 is true.

According to statement 1 :

2^m x 3ⁿ = (2 + 3)^{m + n}, where m, n are positive integers.

This statement does not reflect any general law of exponents.

∴ Statement 1 is false.

According to statement 2 :

If a is a rational number, and m, n are integers, then a^m.aⁿ = a^{m + n}

This is one of the fundamental laws of exponents. It holds for any rational base, and all integer exponents.

∴ Statement 2 is true.

Hence, option 4 is the correct option.