Exponents - whole number bases (2) | Worsheets library - Free Printable

Let's solve each of the exponent problems on this worksheet step by step. The goal is to evaluate each expression with a whole number base and a given exponent.

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1. 7¹ = ?

Any number raised to the power of 1 is the number itself.

Answer:
7¹ = 7

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2. 52² = ?

This means 52 × 52.

Let’s compute:
```
52
× 52
-----
104 ← 52 × 2
260 ← 52 × 50 (shifted one place left)
-----
2704
```

Answer:
52² = 2704

---

3. 99⁴ = ?

This is more complex. We can break it down step by step.

First, calculate 99²:
```
99² = 99 × 99
= (100 - 1)²
= 100² - 2×100×1 + 1²
= 10000 - 200 + 1 = 9801
```

Now, 99⁴ = (99²)² = 9801²

Now compute 9801²:

We can use the identity:
(a - b)² = a² - 2ab + b², where a = 10000, b = 99

But easier: just multiply 9801 × 9801.

Alternatively, use approximation or direct multiplication.

But since this is a large number, let’s do it carefully:

```
9801
× 9801
-------
9801 ← 9801 × 1
0 ← 9801 × 0 (tens place)
78408 ← 9801 × 80 (hundreds place, shifted)
88209 ← 9801 × 9000 (shifted)
---------
```

Actually, better to do:

9801² = (10000 - 199)² → not helpful.

Use:

(9800 + 1)² = 9800² + 2×9800×1 + 1²
= 96040000 + 19600 + 1 = 96059601

Wait — that’s not correct because 9800² = (98 × 100)² = 98² × 10000

Better:
9800² = (98 × 100)² = 98² × 10000

98² = (100 - 2)² = 10000 - 400 + 4 = 9604

So 9800² = 9604 × 10000 = 96,040,000

Then:

(9800 + 1)² = 9800² + 2×9800×1 + 1²
= 96,040,000 + 19,600 + 1 = 96,059,601

✔ So 99⁴ = 96,059,601

Answer:
99⁴ = 96,059,601

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4. 78² = ?

78² = (80 - 2)² = 80² - 2×80×2 + 4 = 6400 - 320 + 4 = 6084

Or: 78 × 78

```
78
× 78
----
624 ← 78 × 8
546 ← 78 × 70
----
6084
```

Answer:
78² = 6084

---

5. 8³ = ?

8³ = 8 × 8 × 8 = 64 × 8 = 512

Answer:
8³ = 512

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6. 80³ = ?

80³ = 80 × 80 × 80

First: 80² = 6400
Then: 6400 × 80 = ?

6400 × 80 = 6400 × 8 × 10 = (51200) × 10 = 512,000

Answer:
80³ = 512,000

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7. 98¹ = ?

Any number to the power of 1 is itself.

Answer:
98¹ = 98

---

8. 15¹ = ?

Same rule.

Answer:
15¹ = 15

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9. 7⁷ = ?

This is a big one. Let’s compute step by step.

We’ll build up powers of 7:

- 7¹ = 7
- 7² = 49
- 7³ = 7 × 49 = 343
- 7⁴ = 7 × 343 = 2401
- 7⁵ = 7 × 2401 = 16,807
- 7⁶ = 7 × 16,807 = 117,649
- 7⁷ = 7 × 117,649 = ?

Now compute:
7 × 117,649

Break it down:

7 × 100,000 = 700,000
7 × 17,000 = 119,000
7 × 600 = 4,200
7 × 40 = 280
7 × 9 = 63

Add them:

700,000
+119,000 = 819,000
+4,200 = 823,200
+280 = 823,480
+63 = 823,543

✔ So 7⁷ = 823,543

Answer:
7⁷ = 823,543

---

10. 55² = ?

55² = (50 + 5)² = 50² + 2×50×5 + 5² = 2500 + 500 + 25 = 3025

Or: 55 × 55

```
55
× 55
----
275
275
----
3025
```

Answer:
55² = 3025

---

11. 67² = ?

67² = (70 - 3)² = 70² - 2×70×3 + 9 = 4900 - 420 + 9 = 4489

Check:
67 × 67

```
67
× 67
----
469 ← 67 × 7
402 ← 67 × 60
----
4489
```

Answer:
67² = 4489

---

12. 50⁴ = ?

50⁴ = (50²)²

50² = 2500
Then 2500² = ?

2500² = (25 × 100)² = 25² × 10000 = 625 × 10000 = 6,250,000

Or: 2500 × 2500

```
2500
× 2500
------
12500
12500
------
6,250,000
```

Answer:
50⁴ = 6,250,000

---

✔ Final Answers:

1. 7¹ = 7
2. 52² = 2704
3. 99⁴ = 96,059,601
4. 78² = 6084
5. 8³ = 512
6. 80³ = 512,000
7. 98¹ = 98
8. 15¹ = 15
9. 7⁷ = 823,543
10. 55² = 3025
11. 67² = 4489
12. 50⁴ = 6,250,000

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