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Printable exponents worksheet with 20 problems for practice.

Exponents Worksheet with math problems involving powers and bases for students to solve.

Exponents Worksheet with math problems involving powers and bases for students to solve.

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Show Answer Key & Explanations Step-by-step solution for: Free exponents worksheets
Let’s solve each problem one by one. Remember, an exponent means how many times to multiply the base number by itself.

For example:
- 4⁴ = 4 × 4 × 4 × 4
- 2¹⁰ = 2 multiplied by itself 10 times (we’ll calculate that carefully)
- Any number to the power of 1 is just itself.
- 0 to any positive power is 0.
- 1 to any power is always 1.

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1a. 4⁴
= 4 × 4 × 4 × 4
= 16 × 4 × 4
= 64 × 4
= 256

1b. 19²
= 19 × 19
= (20 - 1) × (20 - 1) = 400 - 40 + 1 = 361

2a. 2¹⁰
We know:
2¹ = 2
2² = 4
2³ = 8
2⁴ = 16
2⁵ = 32
2⁶ = 64
2⁷ = 128
2⁸ = 256
2⁹ = 512
2¹⁰ = 1024

2b. 47²
= 47 × 47
Break it down:
(50 - 3)² = 50² - 2×50×3 + 3² = 2500 - 300 + 9 = 2209

3a. 2¹
Any number to the power of 1 is itself → 2

3b. 8¹
Same rule → 8

4a. 0²³
Zero to any positive power is zero → 0

4b. 1000³
= 1000 × 1000 × 1000
= 1,000,000 × 1000 = 1,000,000,000 (one billion)

5a. 1⁶
One to any power is always 1 → 1

5b. 1²⁶
Still 1 → 1

6a. 7²
= 7 × 7 = 49

6b. 3³
= 3 × 3 × 3 = 9 × 3 = 27

7a. 87²
Use (90 - 3)² = 90² - 2×90×3 + 3² = 8100 - 540 + 9 = 7569

7b. 2⁷
From earlier: 2⁶ = 64, so 2⁷ = 64 × 2 = 128

8a. 63²
(60 + 3)² = 60² + 2×60×3 + 3² = 3600 + 360 + 9 = 3969

8b. 8²
= 8 × 8 = 64

9a. 0⁷³
Again, 0 to any positive power = 0

9b. 37²
(40 - 3)² = 1600 - 240 + 9 = 1369

10a. 5⁴
= 5 × 5 × 5 × 5 = 25 × 25 = 625

10b. 31¹
Power of 1 → 31

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Final Answer:
1a. 256
1b. 361
2a. 1024
2b. 2209
3a. 2
3b. 8
4a. 0
4b. 1000000000
5a. 1
5b. 1
6a. 49
6b. 27
7a. 7569
7b. 128
8a. 3969
8b. 64
9a. 0
9b. 1369
10a. 625
10b. 31
Parent Tip: Review the logic above to help your child master the concept of exponential form worksheet.
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