To solve the given expression:

$9 + 7.38 \div 0.6 - 1.4^2$

we will follow the correct order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Step-by-step solution:

1. Exponents: First, we calculate $1.4^2$. $1.4^2 = 1.4 \times 1.4 = 1.96$

   So, the expression now becomes: $9 + 7.38 \div 0.6 - 1.96$

2. Division: Next, we handle the division $7.38 \div 0.6$. $7.38 \div 0.6 = 12.3$

   Now, the expression is: $9 + 12.3 - 1.96$

3. Addition and Subtraction: Now, we proceed from left to right, first adding and then subtracting: $9 + 12.3 = 21.3$ $21.3 - 1.96 = 19.34$

Thus, the final answer is:

$\boxed{19.34}$

Would you like further clarification on any step, or do you have any questions?

Here are some related problems you might want to try:

1. Evaluate $5 + 6.5 \div 2 - 3^2$.
2. Simplify $12.4 + 8.6 \div 0.2 - 4^2$.
3. Solve $7.2 \div 0.3 + 2.8 - 1.5^2$.
4. Compute $6.5 + 9.3 \div 1.1 - 2^3$.
5. Calculate $10 + 7.8 \div 0.5 - 5^2$.

Tip: Always deal with exponents and division before moving to addition or subtraction to avoid mistakes!