Exponents Practice Worksheet for students to solve exponent problems.

Let's solve each problem step by step on the Exponents Practice Worksheet.

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Part 1: Work out the given exponents

We'll evaluate each expression using exponent rules:

1. $ 5^4 = 5 \times 5 \times 5 \times 5 = 625 $

2. $ 8^2 = 8 \times 8 = 64 $

3. $ 1^4 = 1 \times 1 \times 1 \times 1 = 1 $

4. $ 10^3 = 10 \times 10 \times 10 = 1000 $

5. $ 6^3 = 6 \times 6 \times 6 = 216 $

6. $ 3^3 = 3 \times 3 \times 3 = 27 $

7. $ 6^2 + 3^2 = (6 \times 6) + (3 \times 3) = 36 + 9 = 45 $

8. $ 10^2 - 5^2 = (10 \times 10) - (5 \times 5) = 100 - 25 = 75 $

9. $ 8^2 - 6^2 = (8 \times 8) - (6 \times 6) = 64 - 36 = 28 $

10. $ 3^3 + 6^2 = (3 \times 3 \times 3) + (6 \times 6) = 27 + 36 = 63 $

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Part 2: Evaluate

Now let’s evaluate the expressions with mixed operations and special cases like powers of 0 and 1.

11. $ 6^2 - 20^1 = (6 \times 6) - 20 = 36 - 20 = 16 $

12. $ 6^2 \times 1^{101} = 36 \times 1 = 36 $
*(Any number to any power is still 1 if the base is 1)*

13. $ 0^8 - 1^{15} = 0 - 1 = -1 $
*(Any non-zero number to any power is itself, but $0^n = 0$ for $n > 0$)*

14. $ 1^{13} - 9^1 = 1 - 9 = -8 $

15. $ 4^2 - 2^2 = (4 \times 4) - (2 \times 2) = 16 - 4 = 12 $

16. $ 5^3 - 3^3 = (5 \times 5 \times 5) - (3 \times 3 \times 3) = 125 - 27 = 98 $

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✔ Final Answers:

#### Part 1:
1. $ 625 $
2. $ 64 $
3. $ 1 $
4. $ 1000 $
5. $ 216 $
6. $ 27 $
7. $ 36 + 9 = 45 $
8. $ 100 - 25 = 75 $
9. $ 64 - 36 = 28 $
10. $ 27 + 36 = 63 $

#### Part 2:
11. $ 16 $
12. $ 36 $
13. $ -1 $
14. $ -8 $
15. $ 12 $
16. $ 98 $

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🔍 Explanation Summary:

- Exponent means repeated multiplication: $ a^n = a \times a \times \ldots \times a $ ($ n $ times).
- Remember: $ 1^n = 1 $, $ 0^n = 0 $ (for $ n > 0 $), and $ a^1 = a $.
- Always follow order of operations (PEMDAS): compute exponents before addition/subtraction.

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