Order of Operations practice worksheet with expressions involving exponents, parentheses, and negative numbers.

Let's solve each expression step by step using the order of operations, often remembered by the acronym PEMDAS:

- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)

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1. $(-5)^2 - 2 \times (-9) + 6$

- Exponent: $(-5)^2 = 25$
- Multiplication: $2 \times (-9) = -18$
- Now: $25 - (-18) + 6 = 25 + 18 + 6 = 49$

✔ Answer: 49

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2. $3 \times 10 + 8 - 4^2$

- Exponent: $4^2 = 16$
- Multiplication: $3 \times 10 = 30$
- Now: $30 + 8 - 16 = 38 - 16 = 22$

✔ Answer: 22

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3. $(-9) - (-8) + 2 \times 4^2$

- Exponent: $4^2 = 16$
- Multiplication: $2 \times 16 = 32$
- Now: $-9 - (-8) + 32 = -9 + 8 + 32 = -1 + 32 = 31$

✔ Answer: 31

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4. $(-3)^3 - 2 + 8 \div (-8)$

- Exponent: $(-3)^3 = -27$
- Division: $8 \div (-8) = -1$
- Now: $-27 - 2 + (-1) = -29 - 1 = -30$

✔ Answer: -30

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5. $8 \div (-4) \times (-6)^2 + 7$

- Exponent: $(-6)^2 = 36$
- Division: $8 \div (-4) = -2$
- Multiplication: $-2 \times 36 = -72$
- Addition: $-72 + 7 = -65$

✔ Answer: -65

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6. $4 \times (-8) + 6 - (-2)^3$

- Exponent: $(-2)^3 = -8$
- Multiplication: $4 \times (-8) = -32$
- Now: $-32 + 6 - (-8) = -26 + 8 = -18$

✔ Answer: -18

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7. $10 \times 5 - (-6)^2 + (-8)$

- Exponent: $(-6)^2 = 36$
- Multiplication: $10 \times 5 = 50$
- Now: $50 - 36 + (-8) = 14 - 8 = 6$

✔ Answer: 6

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8. $(-5)^2 \times 3 + 5 + 9$

- Exponent: $(-5)^2 = 25$
- Multiplication: $25 \times 3 = 75$
- Now: $75 + 5 + 9 = 89$

✔ Answer: 89

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9. $(10 \div (-5) - (-2)) \times (-3)^2$

- Parentheses first:
- $10 \div (-5) = -2$
- $-2 - (-2) = -2 + 2 = 0$
- Exponent: $(-3)^2 = 9$
- Multiplication: $0 \times 9 = 0$

✔ Answer: 0

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10. $4 \times (-6) \div 8 + 3^3$

- Exponent: $3^3 = 27$
- Multiplication and Division from left to right:
- $4 \times (-6) = -24$
- $-24 \div 8 = -3$
- Addition: $-3 + 27 = 24$

✔ Answer: 24

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✔ Final Answers:

1. 49
2. 22
3. 31
4. -30
5. -65
6. -18
7. 6
8. 89
9. 0
10. 24

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