Math worksheet for practicing order of operations, including problems with exponents and parentheses.

Let's solve each problem on Order of Operations Worksheet #1, following the correct order of operations: PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). We'll go step by step for each problem.

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Problem 1:

3 × (2 × 4³) ÷ 4

- First, evaluate exponent:
$ 4^3 = 64 $
- Then inside parentheses:
$ 2 × 64 = 128 $
- Now:
$ 3 × 128 = 384 $
- Then divide:
$ 384 ÷ 4 = 96 $

✔ Answer: 96

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Problem 2:

(4³ + 2 - 1)

- Exponent:
$ 4^3 = 64 $
- Then:
$ 64 + 2 = 66 $, then $ 66 - 1 = 65 $

✔ Answer: 65

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Problem 3:

(5 × 3) × 1 + 5

- Inside parentheses:
$ 5 × 3 = 15 $
- Then:
$ 15 × 1 = 15 $
- Then:
$ 15 + 5 = 20 $

✔ Answer: 20

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Problem 4:

(7² - 2³ - 6)

- Exponents:
$ 7^2 = 49 $, $ 2^3 = 8 $
- Then:
$ 49 - 8 = 41 $, then $ 41 - 6 = 35 $

✔ Answer: 35

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Problem 5:

(5³ + 7) × 2

- Exponent:
$ 5^3 = 125 $
- Add:
$ 125 + 7 = 132 $
- Multiply:
$ 132 × 2 = 264 $

✔ Answer: 264

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Problem 6:

4 - (9 + 2² ÷ 2)

- Exponent:
$ 2^2 = 4 $
- Division:
$ 4 ÷ 2 = 2 $
- Inside parentheses:
$ 9 + 2 = 11 $
- Then:
$ 4 - 11 = -7 $

✔ Answer: -7

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Problem 7:

6 - (9 + 8² × 1³) + 5

- Exponents:
$ 8^2 = 64 $, $ 1^3 = 1 $
- Multiplication:
$ 64 × 1 = 64 $
- Inside parentheses:
$ 9 + 64 = 73 $
- Now:
$ 6 - 73 = -67 $, then $ -67 + 5 = -62 $

✔ Answer: -62

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Problem 8:

(2 ÷ 4 × 8)

- Division and multiplication left to right:
$ 2 ÷ 4 = 0.5 $
$ 0.5 × 8 = 4 $

✔ Answer: 4

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Problem 9:

8 - (3 + 4³) × 5

- Exponent:
$ 4^3 = 64 $
- Inside parentheses:
$ 3 + 64 = 67 $
- Multiply:
$ 67 × 5 = 335 $
- Then:
$ 8 - 335 = -327 $

✔ Answer: -327

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Problem 10:

5 × (2³ - 8) × 5

- Exponent:
$ 2^3 = 8 $
- Inside parentheses:
$ 8 - 8 = 0 $
- Then:
$ 5 × 0 = 0 $, then $ 0 × 5 = 0 $

✔ Answer: 0

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Problem 11:

(9 × 9 + 5)

- Multiplication first:
$ 9 × 9 = 81 $
- Then addition:
$ 81 + 5 = 86 $

✔ Answer: 86

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Problem 12:

(1 + 4 - 4)

- Left to right:
$ 1 + 4 = 5 $, $ 5 - 4 = 1 $

✔ Answer: 1

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Problem 13:

5 × (4 ÷ 1² + 8)

- Exponent:
$ 1^2 = 1 $
- Division:
$ 4 ÷ 1 = 4 $
- Add:
$ 4 + 8 = 12 $
- Multiply:
$ 5 × 12 = 60 $

✔ Answer: 60

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Problem 14:

(5 - 8² + 6 - 1)

- Exponent:
$ 8^2 = 64 $
- Now:
$ 5 - 64 = -59 $, then $ -59 + 6 = -53 $, then $ -53 - 1 = -54 $

✔ Answer: -54

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Problem 15:

2² ÷ (6 ÷ 9) - 5

- Exponent:
$ 2^2 = 4 $
- Division in parentheses:
$ 6 ÷ 9 = \frac{2}{3} $
- Now:
$ 4 ÷ \frac{2}{3} = 4 × \frac{3}{2} = 6 $
- Then:
$ 6 - 5 = 1 $

✔ Answer: 1

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Problem 16:

(3 + 1² + 4)

- Exponent:
$ 1^2 = 1 $
- Then:
$ 3 + 1 = 4 $, $ 4 + 4 = 8 $

✔ Answer: 8

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Problem 17:

1³ - (2 + 3 + 7) × 5

- Exponent:
$ 1^3 = 1 $
- Inside parentheses:
$ 2 + 3 + 7 = 12 $
- Multiply:
$ 12 × 5 = 60 $
- Then:
$ 1 - 60 = -59 $

✔ Answer: -59

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Problem 18:

3 × (2³ + 5) + 2

- Exponent:
$ 2^3 = 8 $
- Inside parentheses:
$ 8 + 5 = 13 $
- Multiply:
$ 3 × 13 = 39 $
- Then:
$ 39 + 2 = 41 $

✔ Answer: 41

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Problem 19:

9 × (2³ ÷ 4 × 5)

- Exponent:
$ 2^3 = 8 $
- Division and multiplication left to right:
$ 8 ÷ 4 = 2 $, then $ 2 × 5 = 10 $
- Then:
$ 9 × 10 = 90 $

✔ Answer: 90

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Problem 20:

(8 + 7 + 2 - 9)

- Left to right:
$ 8 + 7 = 15 $, $ 15 + 2 = 17 $, $ 17 - 9 = 8 $

✔ Answer: 8

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | 96 |
| 2 | 65 |
| 3 | 20 |
| 4 | 35 |
| 5 | 264 |
| 6 | -7 |
| 7 | -62 |
| 8 | 4 |
| 9 | -327 |
| 10 | 0 |
| 11 | 86 |
| 12 | 1 |
| 13 | 60 |
| 14 | -54 |
| 15 | 1 |
| 16 | 8 |
| 17 | -59 |
| 18 | 41 |
| 19 | 90 |
| 20 | 8 |

> ⚠️ Note: The answer key provided at the bottom only shows answers for problems 1 and 2, but we’ve solved all 20 correctly using PEMDAS.

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