Let's break down the given expression step-by-step:

$\left( \frac{ \left( 100 + \left( 14 + 6 \right)^2 \right) }{50} - 8 + \frac{14}{2} \right) / 3 - 3$

Step 1: Simplify the inner parentheses

$14 + 6 = 20$ So the expression becomes: $\left( \frac{ \left( 100 + 20^2 \right) }{50} - 8 + \frac{14}{2} \right) / 3 - 3$

Step 2: Simplify $20^2$

$20^2 = 400$ Now the expression is: $\left( \frac{ \left( 100 + 400 \right) }{50} - 8 + \frac{14}{2} \right) / 3 - 3$

Step 3: Simplify inside the parentheses

$100 + 400 = 500$ Now it becomes: $\left( \frac{500}{50} - 8 + \frac{14}{2} \right) / 3 - 3$

Step 4: Divide 500 by 50

$\frac{500}{50} = 10$ So the expression becomes: $\left( 10 - 8 + \frac{14}{2} \right) / 3 - 3$

Step 5: Simplify $\frac{14}{2}$

$\frac{14}{2} = 7$ Now we have: $\left( 10 - 8 + 7 \right) / 3 - 3$

Step 6: Simplify inside the parentheses

$10 - 8 + 7 = 9$ So the expression is: $\frac{9}{3} - 3$

Step 7: Divide 9 by 3

$\frac{9}{3} = 3$ Now we have: $3 - 3$

Step 8: Subtract

$3 - 3 = 0$

So, the simplified result of the expression is:

$\boxed{0}$

Would you like a further breakdown or have any questions on this? Here are some additional questions you might find helpful:

1. How would the result change if the division by 50 happened first?
2. What is the order of operations (PEMDAS) that guided this simplification?
3. How can we handle exponents in similar expressions with more terms?
4. What if we substituted different numbers inside the parentheses—how would that affect the outcome?
5. What is the importance of simplifying expressions step-by-step in algebra?

Tip: Always remember to simplify inside the innermost parentheses first and follow the order of operations (PEMDAS) to avoid mistakes.