Exponents Worksheet with 20 problems for students to solve, including powers of numbers like 2¹, 5², 3³, and others, designed for educational use.

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

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Understanding Exponents

An exponent tells you how many times to multiply a number (the base) by itself.
For example:
- $ 2^3 = 2 \times 2 \times 2 = 8 $

Special cases:
- Any number raised to the power of 1 is itself: $ a^1 = a $
- Any non-zero number raised to the power of 0 is 1: $ a^0 = 1 $ (but $ 0^0 $ is undefined)
- $ 0^n = 0 $ for any positive $ n $
- $ 1^n = 1 $ for any $ n $

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Now, let’s solve each problem:

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1 a. $ 2^1 $

$ = 2 $
(Any number to the power of 1 is itself)

✔ Answer: 2

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1 b. $ 5^2 $

$ = 5 \times 5 = 25 $

✔ Answer: 25

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2 a. $ 3^3 $

$ = 3 \times 3 \times 3 = 27 $

✔ Answer: 27

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2 b. $ 8^2 $

$ = 8 \times 8 = 64 $

✔ Answer: 64

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3 a. $ 0^{82} $

Zero raised to any positive power is 0.

✔ Answer: 0

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3 b. $ 100^1 $

Any number to the power of 1 is itself.

✔ Answer: 100

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4 a. $ 10^7 $

$ = 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 = 10,000,000 $

✔ Answer: 10,000,000

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4 b. $ 0^{20} $

Again, zero to any positive power is 0.

✔ Answer: 0

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5 a. $ 8^1 $

Any number to the first power is itself.

✔ Answer: 8

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5 b. $ 5^1 $

Same rule.

✔ Answer: 5

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6 a. $ 10^4 $

$ = 10 \times 10 \times 10 \times 10 = 10,000 $

✔ Answer: 10,000

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6 b. $ 6^2 $

$ = 6 \times 6 = 36 $

✔ Answer: 36

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7 a. $ 4^2 $

$ = 4 \times 4 = 16 $

✔ Answer: 16

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7 b. $ 7^2 $

$ = 7 \times 7 = 49 $

✔ Answer: 49

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8 a. $ 100^6 $

This is a large number:
$ = 100 \times 100 \times 100 \times 100 \times 100 \times 100 $
Since $ 100 = 10^2 $, then $ 100^6 = (10^2)^6 = 10^{12} $
So it's $ 1,000,000,000,000 $ (1 trillion)

✔ Answer: 1,000,000,000,000

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8 b. $ 1^9 $

One raised to any power is always 1.

✔ Answer: 1

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9 a. $ 9^2 $

$ = 9 \times 9 = 81 $

✔ Answer: 81

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9 b. $ 1^{99} $

Again, 1 to any power is 1.

✔ Answer: 1

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10 a. $ 100^2 $

$ = 100 \times 100 = 10,000 $

✔ Answer: 10,000

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10 b. $ 2^3 $

$ = 2 \times 2 \times 2 = 8 $

✔ Answer: 8

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✔ Final Answers:

| Problem | Answer |
|--------|---------------|
| 1 a | 2 |
| 1 b | 25 |
| 2 a | 27 |
| 2 b | 64 |
| 3 a | 0 |
| 3 b | 100 |
| 4 a | 10,000,000 |
| 4 b | 0 |
| 5 a | 8 |
| 5 b | 5 |
| 6 a | 10,000 |
| 6 b | 36 |
| 7 a | 16 |
| 7 b | 49 |
| 8 a | 1,000,000,000,000 |
| 8 b | 1 |
| 9 a | 81 |
| 9 b | 1 |
| 10 a | 10,000 |
| 10 b | 8 |

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