Order of operations - worksheet no.7 | Worksheets | Math Center - Free Printable

Problem: Solve the given problems following the Order of Operations (PEMDAS/BODMAS rules):

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

Let's solve each problem step by step.

---

1. \( (-5 + 1)^2 = (-2)^2 \)

#### Step-by-Step Solution:
1. Simplify inside the parentheses:
\[
-5 + 1 = -4
\]
So, the expression becomes:
\[
(-4)^2 = (-2)^2
\]

2. Calculate the exponents:
\[
(-4)^2 = 16 \quad \text{and} \quad (-2)^2 = 4
\]

3. Compare the results:
\[
16 \neq 4
\]

Final Answer:
\[
\boxed{16 \neq 4}
\]

---

2. \( (-9^2) \div (-3) \)

#### Step-by-Step Solution:
1. Calculate the exponent first:
\[
9^2 = 81
\]
Since the negative sign is outside the exponent, we have:
\[
-9^2 = -81
\]

2. Perform the division:
\[
\frac{-81}{-3} = 27
\]

Final Answer:
\[
\boxed{27}
\]

---

3. \( 2 \times (10 - 3^2) \)

#### Step-by-Step Solution:
1. Simplify inside the parentheses:
- Calculate the exponent first:
\[
3^2 = 9
\]
- Subtract:
\[
10 - 9 = 1
\]
So, the expression becomes:
\[
2 \times 1
\]

2. Perform the multiplication:
\[
2 \times 1 = 2
\]

Final Answer:
\[
\boxed{2}
\]

---

4. \( (4 - 6)^2 \div (-1) \)

#### Step-by-Step Solution:
1. Simplify inside the parentheses:
\[
4 - 6 = -2
\]
So, the expression becomes:
\[
(-2)^2 \div (-1)
\]

2. Calculate the exponent:
\[
(-2)^2 = 4
\]
So, the expression becomes:
\[
4 \div (-1)
\]

3. Perform the division:
\[
4 \div (-1) = -4
\]

Final Answer:
\[
\boxed{-4}
\]

---

5. \( (12 - 16)^2 \times (-1)^{21} \)

#### Step-by-Step Solution:
1. Simplify inside the parentheses:
\[
12 - 16 = -4
\]
So, the expression becomes:
\[
(-4)^2 \times (-1)^{21}
\]

2. Calculate the exponents:
- For \((-4)^2\):
\[
(-4)^2 = 16
\]
- For \((-1)^{21}\):
Since the exponent is odd, \((-1)^{21} = -1\)
So, the expression becomes:
\[
16 \times (-1)
\]

3. Perform the multiplication:
\[
16 \times (-1) = -16
\]

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

---

6. \( (1 - 2 \times 1)^2 \div (-2^2) \)

#### Step-by-Step Solution:
1. Simplify inside the parentheses:
- Follow the order of operations inside the parentheses:
\[
2 \times 1 = 2
\]
So:
\[
1 - 2 = -1
\]
The expression becomes:
\[
(-1)^2 \div (-2^2)
\]

2. Calculate the exponents:
- For \((-1)^2\):
\[
(-1)^2 = 1
\]
- For \((-2^2)\):
Since the negative sign is not part of the base, we have:
\[
-2^2 = -(2^2) = -4
\]
So, the expression becomes:
\[
1 \div (-4)
\]

3. Perform the division:
\[
1 \div (-4) = -\frac{1}{4}
\]

Final Answer:
\[
\boxed{-\frac{1}{4}}
\]

---

7. \( 28 - 16 \div 2^2 \)

#### Step-by-Step Solution:
1. Calculate the exponent:
\[
2^2 = 4
\]
So, the expression becomes:
\[
28 - 16 \div 4
\]

2. Perform the division:
\[
16 \div 4 = 4
\]
So, the expression becomes:
\[
28 - 4
\]

3. Perform the subtraction:
\[
28 - 4 = 24
\]

Final Answer:
\[
\boxed{24}
\]

---

8. \( 3^2 - 5 \times 3 + 3 \)

#### Step-by-Step Solution:
1. Calculate the exponent:
\[
3^2 = 9
\]
So, the expression becomes:
\[
9 - 5 \times 3 + 3
\]

2. Perform the multiplication:
\[
5 \times 3 = 15
\]
So, the expression becomes:
\[
9 - 15 + 3
\]

3. Perform the addition and subtraction from left to right:
\[
9 - 15 = -6
\]
\[
-6 + 3 = -3
\]

Final Answer:
\[
\boxed{-3}
\]

---

9. \( (-10)^2 \div (-5)^2 \)

#### Step-by-Step Solution:
1. Calculate the exponents:
- For \((-10)^2\):
\[
(-10)^2 = 100
\]
- For \((-5)^2\):
\[
(-5)^2 = 25
\]
So, the expression becomes:
\[
\frac{100}{25}
\]

2. Perform the division:
\[
\frac{100}{25} = 4
\]

Final Answer:
\[
\boxed{4}
\]

---

10. \( 27 + (9^2 \div 3^2) \)

#### Step-by-Step Solution:
1. Calculate the exponents:
- For \(9^2\):
\[
9^2 = 81
\]
- For \(3^2\):
\[
3^2 = 9
\]
So, the expression becomes:
\[
27 + \left( \frac{81}{9} \right)
\]

2. Perform the division:
\[
\frac{81}{9} = 9
\]
So, the expression becomes:
\[
27 + 9
\]

3. Perform the addition:
\[
27 + 9 = 36
\]

Final Answer:
\[
\boxed{36}
\]

---

11. \( 15 - (3 - 2 \times 4)^2 \)

#### Step-by-Step Solution:
1. Simplify inside the parentheses:
- Follow the order of operations inside the parentheses:
\[
2 \times 4 = 8
\]
So:
\[
3 - 8 = -5
\]
The expression becomes:
\[
15 - (-5)^2
\]

2. Calculate the exponent:
\[
(-5)^2 = 25
\]
So, the expression becomes:
\[
15 - 25
\]

3. Perform the subtraction:
\[
15 - 25 = -10
\]

Final Answer:
\[
\boxed{-10}
\]

---

12. \( (-4)^2 \div (-2)^3 + 3 \times 5^2 \)

#### Step-by-Step Solution:
1. Calculate the exponents:
- For \((-4)^2\):
\[
(-4)^2 = 16
\]
- For \((-2)^3\):
\[
(-2)^3 = -8
\]
- For \(5^2\):
\[
5^2 = 25
\]
So, the expression becomes:
\[
\frac{16}{-8} + 3 \times 25
\]

2. Perform the division and multiplication:
- Division:
\[
\frac{16}{-8} = -2
\]
- Multiplication:
\[
3 \times 25 = 75
\]
So, the expression becomes:
\[
-2 + 75
\]

3. Perform the addition:
\[
-2 + 75 = 73
\]

Final Answer:
\[
\boxed{73}
\]

---

Final Answers:

1. \( \boxed{16 \neq 4} \)
2. \( \boxed{27} \)
3. \( \boxed{2} \)
4. \( \boxed{-4} \)
5. \( \boxed{-16} \)
6. \( \boxed{-\frac{1}{4}} \)
7. \( \boxed{24} \)
8. \( \boxed{-3} \)
9. \( \boxed{4} \)
10. \( \boxed{36} \)
11. \( \boxed{-10} \)
12. \( \boxed{73} \)