How do you simplify #3+ ( 4- ( 6- ( 1- 6- - 16\div 4) ) ) \cdot - 5#?

There is one rule in order of operations, follow BODMAS. Brackets (do the deepest level of brackets first), then orders (for example powers), followed by division, multiplication, addition and finally subtraction.

Deepest level of bracket first;

Note that even with that bracket, we follow BODMAS and do the division before subtraction

Then the next level of bracket;

Then the final, outermost set of brackets;

Count the number of terms first. There are 2 terms - keep them separate until the last step. Start by removing the innermost brackets each time.

To simplify the expression (3 + (4 - (6 - (1 - 6 - (-16 \div 4))) \cdot -5), follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):

1. Start with the innermost parentheses and work outward.
2. Simplify inside each set of parentheses.
3. Perform multiplication and division from left to right.
4. Perform addition and subtraction from left to right.

First, solve inside the innermost parentheses:

((-16 \div 4) = -4)

Next, simplify inside the parentheses:

(1 - 6 - (-4) = 1 - 6 + 4 = -1)

Next, simplify inside the parentheses:

(6 - (-1) = 6 + 1 = 7)

Now, simplify inside the parentheses:

(4 - 7 = -3)

Now, multiply by -5:

(-3 \cdot -5 = 15)

Finally, add 3:

(3 + 15 = 18)

So, (3 + (4 - (6 - (1 - 6 - (-16 \div 4))) \cdot -5 = 18).