Advanced Order of Operations math worksheet with 12 expressions to evaluate.

To solve the given expressions, we need to follow the order of operations, often remembered by the acronym PEMDAS:

1. Parentheses/Brackets
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Let's evaluate each expression step by step.

---

Expression 1:

\[
\left[(-96) \div (-4)^3 - (-11)\right] \cdot (-9)
\]

#### Step 1: Evaluate the exponent.
\[
(-4)^3 = (-4) \cdot (-4) \cdot (-4) = -64
\]

#### Step 2: Perform the division.
\[
-96 \div (-64) = \frac{-96}{-64} = \frac{3}{2} = 1.5
\]

#### Step 3: Simplify inside the brackets.
\[
1.5 - (-11) = 1.5 + 11 = 12.5
\]

#### Step 4: Multiply by \(-9\).
\[
12.5 \cdot (-9) = -112.5
\]

Answer:
\[
\boxed{-112.5}
\]

---

Expression 2:

\[
\left[(-4) + (8 + 4)\right] \cdot (-5)^2 - 7
\]

#### Step 1: Simplify inside the inner parentheses.
\[
8 + 4 = 12
\]

#### Step 2: Simplify inside the brackets.
\[
(-4) + 12 = 8
\]

#### Step 3: Evaluate the exponent.
\[
(-5)^2 = 25
\]

#### Step 4: Multiply.
\[
8 \cdot 25 = 200
\]

#### Step 5: Subtract 7.
\[
200 - 7 = 193
\]

Answer:
\[
\boxed{193}
\]

---

Expression 3:

\[
(-9) - (-10) \cdot \left[(-4) - ((-4)^2 + (-10))\right]
\]

#### Step 1: Evaluate the exponent.
\[
(-4)^2 = 16
\]

#### Step 2: Simplify inside the innermost parentheses.
\[
(-4)^2 + (-10) = 16 - 10 = 6
\]

#### Step 3: Simplify inside the brackets.
\[
(-4) - 6 = -10
\]

#### Step 4: Multiply.
\[
-10 \cdot (-10) = 100
\]

#### Step 5: Subtract.
\[
-9 - 100 = -109
\]

Answer:
\[
\boxed{-109}
\]

---

Expression 4:

\[
\left[10 - (5^2 - 10)\right] \cdot (5 - 4)
\]

#### Step 1: Evaluate the exponent.
\[
5^2 = 25
\]

#### Step 2: Simplify inside the inner parentheses.
\[
25 - 10 = 15
\]

#### Step 3: Simplify inside the brackets.
\[
10 - 15 = -5
\]

#### Step 4: Simplify the second part.
\[
5 - 4 = 1
\]

#### Step 5: Multiply.
\[
-5 \cdot 1 = -5
\]

Answer:
\[
\boxed{-5}
\]

---

Expression 5:

\[
\left[(-2)^2 + (+8)\right] \div (-9) + (-8)
\]

#### Step 1: Evaluate the exponent.
\[
(-2)^2 = 4
\]

#### Step 2: Simplify inside the brackets.
\[
4 + 8 = 12
\]

#### Step 3: Divide.
\[
12 \div (-9) = -\frac{12}{9} = -\frac{4}{3}
\]

#### Step 4: Add.
\[
-\frac{4}{3} + (-8) = -\frac{4}{3} - 8 = -\frac{4}{3} - \frac{24}{3} = -\frac{28}{3}
\]

Answer:
\[
\boxed{-\frac{28}{3}}
\]

---

Expression 6:

\[
5 - 9 \cdot \left[2 - (2^2 + 9)\right]
\]

#### Step 1: Evaluate the exponent.
\[
2^2 = 4
\]

#### Step 2: Simplify inside the inner parentheses.
\[
2^2 + 9 = 4 + 9 = 13
\]

#### Step 3: Simplify inside the brackets.
\[
2 - 13 = -11
\]

#### Step 4: Multiply.
\[
9 \cdot (-11) = -99
\]

#### Step 5: Subtract.
\[
5 - (-99) = 5 + 99 = 104
\]

Answer:
\[
\boxed{104}
\]

---

Expression 7:

\[
\left[(-3) - (5^2 - 3)\right] \cdot (5 - (-8))
\]

#### Step 1: Evaluate the exponent.
\[
5^2 = 25
\]

#### Step 2: Simplify inside the inner parentheses.
\[
5^2 - 3 = 25 - 3 = 22
\]

#### Step 3: Simplify inside the brackets.
\[
(-3) - 22 = -25
\]

#### Step 4: Simplify the second part.
\[
5 - (-8) = 5 + 8 = 13
\]

#### Step 5: Multiply.
\[
-25 \cdot 13 = -325
\]

Answer:
\[
\boxed{-325}
\]

---

Expression 8:

\[
\left[8 + (14 \div 7)\right] \cdot 4^2 \div 2
\]

#### Step 1: Perform the division.
\[
14 \div 7 = 2
\]

#### Step 2: Simplify inside the brackets.
\[
8 + 2 = 10
\]

#### Step 3: Evaluate the exponent.
\[
4^2 = 16
\]

#### Step 4: Multiply.
\[
10 \cdot 16 = 160
\]

#### Step 5: Divide.
\[
160 \div 2 = 80
\]

Answer:
\[
\boxed{80}
\]

---

Expression 9:

\[
\left[(-2) + ((-4) \div (-2))\right] \cdot (-5)^2 - (-7)
\]

#### Step 1: Perform the division.
\[
(-4) \div (-2) = 2
\]

#### Step 2: Simplify inside the brackets.
\[
(-2) + 2 = 0
\]

#### Step 3: Evaluate the exponent.
\[
(-5)^2 = 25
\]

#### Step 4: Multiply.
\[
0 \cdot 25 = 0
\]

#### Step 5: Subtract.
\[
0 - (-7) = 0 + 7 = 7
\]

Answer:
\[
\boxed{7}
\]

---

Expression 10:

\[
3 - 7 \cdot \left[4 - (4^3 + 7)\right]
\]

#### Step 1: Evaluate the exponent.
\[
4^3 = 64
\]

#### Step 2: Simplify inside the inner parentheses.
\[
4^3 + 7 = 64 + 7 = 71
\]

#### Step 3: Simplify inside the brackets.
\[
4 - 71 = -67
\]

#### Step 4: Multiply.
\[
7 \cdot (-67) = -469
\]

#### Step 5: Subtract.
\[
3 - (-469) = 3 + 469 = 472
\]

Answer:
\[
\boxed{472}
\]

---

Expression 11:

\[
\left[(-8) + (14 \div (-7))\right] \cdot 2^2 \cdot (-2)
\]

#### Step 1: Perform the division.
\[
14 \div (-7) = -2
\]

#### Step 2: Simplify inside the brackets.
\[
(-8) + (-2) = -10
\]

#### Step 3: Evaluate the exponent.
\[
2^2 = 4
\]

#### Step 4: Multiply.
\[
-10 \cdot 4 = -40
\]

#### Step 5: Multiply again.
\[
-40 \cdot (-2) = 80
\]

Answer:
\[
\boxed{80}
\]

---

Expression 12:

\[
\left[\left((-96) \div (-4)\right)^2 - (-11)\right] \cdot (-6) + (-6)
\]

#### Step 1: Perform the division.
\[
(-96) \div (-4) = 24
\]

#### Step 2: Evaluate the exponent.
\[
24^2 = 576
\]

#### Step 3: Simplify inside the brackets.
\[
576 - (-11) = 576 + 11 = 587
\]

#### Step 4: Multiply.
\[
587 \cdot (-6) = -3522
\]

#### Step 5: Add.
\[
-3522 + (-6) = -3522 - 6 = -3528
\]

Answer:
\[
\boxed{-3528}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ -112.5 \\
2. & \ 193 \\
3. & \ -109 \\
4. & \ -5 \\
5. & \ -\frac{28}{3} \\
6. & \ 104 \\
7. & \ -325 \\
8. & \ 80 \\
9. & \ 7 \\
10. & \ 472 \\
11. & \ 80 \\
12. & \ -3528 \\
\end{aligned}
}
\]