To solve the expression $7 + 3 \times 7 + 9 \times 2^2$, follow the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. Exponentiation: $2^2 = 4$

2. Multiplication: $3 \times 7 = 21$ $9 \times 4 = 36$

3. Addition: $7 + 21 + 36 = 64$

So, the value of the expression is $\boxed{64}$.

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. What happens if you change the exponent in the expression $2^2$ to $2^3$?
2. How would the result change if the multiplication and addition were rearranged without parentheses?
3. Can you express $7 + 3 \times 7 + 9 \times 2^2$ using only addition and subtraction?
4. How does the order of operations affect the outcome in this type of expression?
5. What if the expression included a division operation as well?

Tip: Always handle exponentiation before performing multiplication or division to ensure accurate results.