Let's break down the expression step by step:

\[
-30 + (-10) + \left\{8 + \left[3 - (2)(6) - (-16) \left(\frac{27}{3}\right)\right]\right\}
\]

### Step 1: Simplify the division inside the brackets.
\[
\frac{27}{3} = 9
\]
Now the expression becomes:
\[
-30 + (-10) + \left\{8 + \left[3 - (2)(6) - (-16)(9)\right]\right\}
\]

### Step 2: Multiply the numbers inside the parentheses.
\[
(2)(6) = 12 \quad \text{and} \quad (-16)(9) = -144
\]
Now the expression is:
\[
-30 + (-10) + \left\{8 + \left[3 - 12 - (-144)\right]\right\}
\]

### Step 3: Simplify the inner brackets.
\[
3 - 12 = -9
\quad \text{and} \quad -9 - (-144) = -9 + 144 = 135
\]
Now the expression becomes:
\[
-30 + (-10) + \left\{8 + 135\right\}
\]

### Step 4: Simplify inside the braces.
\[
8 + 135 = 143
\]
So now we have:
\[
-30 + (-10) + 143
\]

### Step 5: Perform the final addition.
\[
-30 + (-10) = -40
\]
\[
-40 + 143 = 103
\]

Thus, the value of the expression is:
\[
\boxed{103}
\]

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

Here are 5 related questions to practice:
1. Simplify: \( -25 + (-15) + \{7 + [4 - (3)(5) - (-10)(6)]\} \)
2. Evaluate: \( 50 + (-20) + \{12 + [10 - (4)(7) - (-14)(8)]\} \)
3. What is the result of \( -40 + (-5) + \{9 + [2 - (3)(8) - (-20)(4)]\} \)?
4. Simplify: \( -12 + (-8) + \{5 + [6 - (5)(7) - (-18)(3)]\} \)
5. Evaluate \( 10 + (-30) + \{15 + [8 - (2)(9) - (-13)(5)]\} \)

**Tip:** Always perform operations inside brackets and parentheses first, following the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

30 + (-10) + {8 + [3 - (2)(6) - (-16)[27/3]]}

Learn how to simplify the expression 30 + (-10) + {8 + [3 - (2)(6) - (-16)[27/3]]} step by step. This problem demonstrates the use of the order of operations (PEMDAS) and handling nested parentheses. Suitable for students in Grades 6-8.

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