Let's solve the expression step-by-step:

1. Simplify the exponent: $-4^2 = -16$

So, the expression now looks like: $-3 - (-16) \times 6 / 3 - (-1)$

2. Simplify the multiplication and division within the parentheses: $-16 \times 6 = -96$ $-96 / 3 = -32$

So, the expression now looks like: $-3 - (-32) - (-1)$

3. Simplify the double negatives: $-3 + 32 + 1$

4. Perform the addition and subtraction: $-3 + 32 = 29$ $29 + 1 = 30$

So, the value of the expression is: $30$

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you handle exponents with negative bases?
2. What is the order of operations (PEMDAS/BODMAS)?
3. How do you simplify expressions with multiple operations?
4. How do you handle negative numbers in arithmetic operations?
5. How do parentheses affect the order of operations?

Tip: Always perform operations inside parentheses first and be mindful of the order of operations (PEMDAS/BODMAS) to avoid mistakes.