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.
---
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
---
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.