Math worksheet focusing on order of operations with parentheses, brackets, and braces.

Let’s solve each problem step by step, following the order of operations: Parentheses first, then Brackets, then Braces — and within those, do exponents, multiplication/division (left to right), addition/subtraction (left to right).

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Problem 1:
2⁴ + {14 - [16 + (39 ÷ 3)]}

Step 1: Innermost parentheses → 39 ÷ 3 = 13
→ Now: 2⁴ + {14 - [16 + 13]}

Step 2: Inside brackets → 16 + 13 = 29
→ Now: 2⁴ + {14 - 29}

Step 3: Exponent → 2⁴ = 16
→ Now: 16 + {14 - 29}

Step 4: Inside braces → 14 - 29 = -15
→ Now: 16 + (-15) = 1

✔ Final Answer for #1: 1

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Problem 2:
5³ + {2² + [27 ÷ (3 × 3)]}

Step 1: Innermost parentheses → 3 × 3 = 9
→ Now: 5³ + {2² + [27 ÷ 9]}

Step 2: Division inside brackets → 27 ÷ 9 = 3
→ Now: 5³ + {2² + 3}

Step 3: Exponents → 5³ = 125, 2² = 4
→ Now: 125 + {4 + 3}

Step 4: Inside braces → 4 + 3 = 7
→ Now: 125 + 7 = 132

✔ Final Answer for #2: 132

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Problem 3:
2 × {3 + [7 × (69 ÷ 23) - 10]}

Step 1: Innermost parentheses → 69 ÷ 23 = 3
→ Now: 2 × {3 + [7 × 3 - 10]}

Step 2: Multiplication inside brackets → 7 × 3 = 21
→ Now: 2 × {3 + [21 - 10]}

Step 3: Subtraction inside brackets → 21 - 10 = 11
→ Now: 2 × {3 + 11}

Step 4: Inside braces → 3 + 11 = 14
→ Now: 2 × 14 = 28

✔ Final Answer for #3: 28

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Problem 4:
(21 × 3) - [(56 ÷ 8) - 2]

Step 1: Parentheses → 21 × 3 = 63
→ Now: 63 - [(56 ÷ 8) - 2]

Step 2: Inside brackets → 56 ÷ 8 = 7
→ Now: 63 - [7 - 2]

Step 3: Inside brackets → 7 - 2 = 5
→ Now: 63 - 5 = 58

✔ Final Answer for #4: 58

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Problem 5:
3 + [6(11 + 1 - 4)] ÷ 8 × 2

Note: “6(...)” means 6 multiplied by what’s in parentheses.

Step 1: Inside parentheses → 11 + 1 - 4 = 8
→ Now: 3 + [6 × 8] ÷ 8 × 2

Step 2: Multiply inside brackets → 6 × 8 = 48
→ Now: 3 + 48 ÷ 8 × 2

Step 3: Division and multiplication left to right → 48 ÷ 8 = 6; then 6 × 2 = 12
→ Now: 3 + 12 = 15

✔ Final Answer for #5: 15

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Problem 6:
2{8² - 7[32 - 4(3² + 1)](-1)}

This one is tricky. Let’s go slow.

Step 1: Innermost parentheses → 3² = 9 → 9 + 1 = 10
→ Now: 2{8² - 7[32 - 4×10](-1)}

Step 2: Multiply inside brackets → 4 × 10 = 40
→ Now: 2{8² - 7[32 - 40](-1)}

Step 3: Inside brackets → 32 - 40 = -8
→ Now: 2{8² - 7[-8](-1)}

Step 4: Handle the multiplication with negatives → 7 × (-8) = -56; then -56 × (-1) = +56
Wait — let’s be careful. The expression is:
-7 × [ -8 ] × (-1)

Actually, it’s: 7 × [ -8 ] × (-1) but there’s a minus sign before the 7? Let’s re-read:

Original: 8² - 7[32 - 4(...)](-1)

So after Step 3: we have 8² - 7 * (-8) * (-1)

Compute that part:
First, 7 × (-8) = -56
Then, -56 × (-1) = +56
But note: it’s subtracted! So it’s: 8² - (that result)

Wait — no: the structure is:

8² - [ 7 × (result of bracket) × (-1) ]

We had: 7 × (-8) × (-1) = 7 × 8 = 56? Let’s compute signs:

Negative times negative = positive → (-8) × (-1) = +8
Then 7 × 8 = 56

So now: 8² - 56

Step 5: 8² = 64 → 64 - 56 = 8

Now multiply by the outer 2: 2 × 8 = 16

Wait — let me double-check the grouping.

Expression: 2{8² - 7[32 - 4(3² + 1)](-1)}

After simplifying inner parts:

= 2{64 - 7[32 - 40](-1)}
= 2{64 - 7[-8](-1)}

Now, 7 × (-8) = -56
Then -56 × (-1) = +56

So: 64 - (+56) = 8? No — wait:

The expression is: 64 minus [7 × (-8) × (-1)]

Which is: 64 - [56] = 8

Then 2 × 8 = 16

Yes.

✔ Final Answer for #6: 16

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Problem 7:
2{1 + [4(2 + 1) + 3]}

Step 1: Innermost parentheses → 2 + 1 = 3
→ Now: 2{1 + [4 × 3 + 3]}

Step 2: Multiply → 4 × 3 = 12
→ Now: 2{1 + [12 + 3]}

Step 3: Add inside brackets → 12 + 3 = 15
→ Now: 2{1 + 15}

Step 4: Inside braces → 1 + 15 = 16
→ Now: 2 × 16 = 32

✔ Final Answer for #7: 32

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Problem 8:
[15 - [3(2 + 1) + 1]] × 4

Step 1: Innermost parentheses → 2 + 1 = 3
→ Now: [15 - [3 × 3 + 1]] × 4

Step 2: Multiply → 3 × 3 = 9
→ Now: [15 - [9 + 1]] × 4

Step 3: Add inside inner brackets → 9 + 1 = 10
→ Now: [15 - 10] × 4

Step 4: Subtract → 15 - 10 = 5
→ Now: 5 × 4 = 20

✔ Final Answer for #8: 20

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Final Answer:
1. 1
2. 132
3. 28
4. 58
5. 15
6. 16
7. 32
8. 20