6-step Order Of Operation With Integers (3) Worksheet - Free Printable

To solve the given expressions using the correct order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), let's simplify each expression step by step.

---

Expression 1:

\[
(4^2 - 7 + (-9))^3 \div (2 \times 8)
\]

#### Step 1: Simplify inside the parentheses.
- Calculate \(4^2\):
\[
4^2 = 16
\]
- Substitute back:
\[
(16 - 7 + (-9))^3 \div (2 \times 8)
\]
- Perform addition and subtraction inside the parentheses:
\[
16 - 7 = 9
\]
\[
9 + (-9) = 0
\]
- So, the expression becomes:
\[
(0)^3 \div (2 \times 8)
\]

#### Step 2: Simplify the exponent.
- Calculate \(0^3\):
\[
0^3 = 0
\]
- So, the expression becomes:
\[
0 \div (2 \times 8)
\]

#### Step 3: Perform multiplication in the denominator.
- Calculate \(2 \times 8\):
\[
2 \times 8 = 16
\]
- So, the expression becomes:
\[
0 \div 16
\]

#### Step 4: Perform division.
- Calculate \(0 \div 16\):
\[
0 \div 16 = 0
\]

#### Final Answer:
\[
\boxed{0}
\]

---

Expression 2:

\[
((-2) - 2^2) \times ((-3) + (-5)) \div ((-9) + 6)
\]

#### Step 1: Simplify inside the parentheses.
- Calculate \(2^2\):
\[
2^2 = 4
\]
- Substitute back:
\[
((-2) - 4) \times ((-3) + (-5)) \div ((-9) + 6)
\]
- Perform subtraction and addition inside the parentheses:
\[
(-2) - 4 = -6
\]
\[
(-3) + (-5) = -8
\]
\[
(-9) + 6 = -3
\]
- So, the expression becomes:
\[
(-6) \times (-8) \div (-3)
\]

#### Step 2: Perform multiplication.
- Calculate \((-6) \times (-8)\):
\[
(-6) \times (-8) = 48
\]
- So, the expression becomes:
\[
48 \div (-3)
\]

#### Step 3: Perform division.
- Calculate \(48 \div (-3)\):
\[
48 \div (-3) = -16
\]

#### Final Answer:
\[
\boxed{-16}
\]

---

Expression 3:

\[
(10 \div ((-7) - (-8))) \times (-10) + 8^2 + (-5)
\]

#### Step 1: Simplify inside the innermost parentheses.
- Calculate \((-7) - (-8)\):
\[
(-7) - (-8) = -7 + 8 = 1
\]
- So, the expression becomes:
\[
(10 \div 1) \times (-10) + 8^2 + (-5)
\]

#### Step 2: Perform division.
- Calculate \(10 \div 1\):
\[
10 \div 1 = 10
\]
- So, the expression becomes:
\[
10 \times (-10) + 8^2 + (-5)
\]

#### Step 3: Perform multiplication.
- Calculate \(10 \times (-10)\):
\[
10 \times (-10) = -100
\]
- So, the expression becomes:
\[
-100 + 8^2 + (-5)
\]

#### Step 4: Simplify the exponent.
- Calculate \(8^2\):
\[
8^2 = 64
\]
- So, the expression becomes:
\[
-100 + 64 + (-5)
\]

#### Step 5: Perform addition and subtraction.
- Calculate \(-100 + 64\):
\[
-100 + 64 = -36
\]
- Then, add \((-5)\):
\[
-36 + (-5) = -41
\]

#### Final Answer:
\[
\boxed{-41}
\]

---

Expression 4:

\[
(((-9) + 9) \times 3) \div (8 - 5)^3 \div 4
\]

#### Step 1: Simplify inside the parentheses.
- Calculate \((-9) + 9\):
\[
(-9) + 9 = 0
\]
- So, the expression becomes:
\[
(0 \times 3) \div (8 - 5)^3 \div 4
\]
- Calculate \(8 - 5\):
\[
8 - 5 = 3
\]
- So, the expression becomes:
\[
(0 \times 3) \div 3^3 \div 4
\]

#### Step 2: Simplify the exponent.
- Calculate \(3^3\):
\[
3^3 = 27
\]
- So, the expression becomes:
\[
(0 \times 3) \div 27 \div 4
\]

#### Step 3: Perform multiplication.
- Calculate \(0 \times 3\):
\[
0 \times 3 = 0
\]
- So, the expression becomes:
\[
0 \div 27 \div 4
\]

#### Step 4: Perform division.
- Calculate \(0 \div 27\):
\[
0 \div 27 = 0
\]
- Then, divide by 4:
\[
0 \div 4 = 0
\]

#### Final Answer:
\[
\boxed{0}
\]

---

Expression 5:

\[
(6 + (-5)) \div (8 - 7) \times (-3) + (-9)^2
\]

#### Step 1: Simplify inside the parentheses.
- Calculate \(6 + (-5)\):
\[
6 + (-5) = 1
\]
- Calculate \(8 - 7\):
\[
8 - 7 = 1
\]
- So, the expression becomes:
\[
1 \div 1 \times (-3) + (-9)^2
\]

#### Step 2: Simplify the exponent.
- Calculate \((-9)^2\):
\[
(-9)^2 = 81
\]
- So, the expression becomes:
\[
1 \div 1 \times (-3) + 81
\]

#### Step 3: Perform division and multiplication from left to right.
- Calculate \(1 \div 1\):
\[
1 \div 1 = 1
\]
- Then, multiply by \((-3)\):
\[
1 \times (-3) = -3
\]
- So, the expression becomes:
\[
-3 + 81
\]

#### Step 4: Perform addition.
- Calculate \(-3 + 81\):
\[
-3 + 81 = 78
\]

#### Final Answer:
\[
\boxed{78}
\]

---

Expression 6:

\[
((-6) \times (10 - 2 + (-8)))^3 \div 8^2
\]

#### Step 1: Simplify inside the parentheses.
- Calculate \(10 - 2 + (-8)\):
\[
10 - 2 = 8
\]
\[
8 + (-8) = 0
\]
- So, the expression becomes:
\[
((-6) \times 0)^3 \div 8^2
\]

#### Step 2: Perform multiplication.
- Calculate \((-6) \times 0\):
\[
(-6) \times 0 = 0
\]
- So, the expression becomes:
\[
(0)^3 \div 8^2
\]

#### Step 3: Simplify the exponent.
- Calculate \(0^3\):
\[
0^3 = 0
\]
- Calculate \(8^2\):
\[
8^2 = 64
\]
- So, the expression becomes:
\[
0 \div 64
\]

#### Step 4: Perform division.
- Calculate \(0 \div 64\):
\[
0 \div 64 = 0
\]

#### Final Answer:
\[
\boxed{0}
\]

---

Final Answers:

\[
\boxed{0, -16, -41, 0, 78, 0}
\]