To simplify the expression $10 - 5|2^3 - 4^2|$, let’s follow these steps:

1. Evaluate the exponents inside the absolute value:

   • $2^3 = 8$
   • $4^2 = 16$

   So the expression inside the absolute value becomes: $2^3 - 4^2 = 8 - 16 = -8$

2. Apply the absolute value: $|2^3 - 4^2| = |-8| = 8$

3. Substitute back and simplify the expression: $10 - 5 \cdot 8$

4. Multiply: $5 \cdot 8 = 40$

5. Subtract: $10 - 40 = -30$

Final Answer:

$10 - 5|2^3 - 4^2| = -30$

Would you like more details on any of these steps, or do you have any questions?

Related Questions

1. How would this change if there were no absolute value symbols?
2. What if $2^3$ and $4^2$ were multiplied instead of subtracted?
3. How do absolute values affect negative results inside an expression?
4. Why is exponentiation performed before multiplication in the order of operations?
5. How would this problem look if written as a function?

Tip:

Remember, the absolute value transforms any negative result inside it to positive before continuing with other operations.