Algebra-2

Question Analysis
This question involves simplifying a power of a product—specifically, squaring a term that combines a constant coefficient (3) and an exponential term ( ).
The main focus is on applying two key rules: the power of a product rule (for the constant and exponential term) and the power rule for exponents (for simplifying the exponential part).

Key Concept Explanation
Power of a Product Rule: For any non-zero numbers a and b, and integer n: .
This means when raising a product to a power, you raise each factor in the product to that power separately.
Power Rule for Exponents: For any non-zero base a, and integers m and n: .
This rule applies to exponential terms: raising an exponent to another power requires multiplying the exponents, while keeping the base unchanged.
Base e Note: Euler’s number (e) follows all standard exponent rules, just like constants (e.g., 2) or variables (e.g., x).

Step-by-step Solution
1. Apply the Power of a Product Rule: Separate the constant (3) and the exponential term ( ), then square each: .
2. Simplify the constant term: Calculate (3 squared): .
3. Apply the Power Rule for Exponents to the exponential term: Multiply the exponents (