Math worksheet for practicing exponent problems with a fun fish illustration.

Let's solve each expression step by step to find the exponent (the number in the blank) that makes the equation true.

We are looking for the exponent such that:

$$
\text{Base}^{\text{Exponent}} = \text{Result}
$$

---

1. $ 2^\square = 16 $

We know:
- $ 2^1 = 2 $
- $ 2^2 = 4 $
- $ 2^3 = 8 $
- $ 2^4 = 16 $

✔ So, $ 2^4 = 16 $ → Exponent = 4

---

2. $ 2^\square = 64 $

Continue powers of 2:
- $ 2^5 = 32 $
- $ 2^6 = 64 $

✔ So, $ 2^6 = 64 $ → Exponent = 6

---

3. $ 3^\square = 81 $

Powers of 3:
- $ 3^1 = 3 $
- $ 3^2 = 9 $
- $ 3^3 = 27 $
- $ 3^4 = 81 $

✔ So, $ 3^4 = 81 $ → Exponent = 4

---

4. $ 9^\square = 81 $

Note: $ 9 = 3^2 $, so we can write:
- $ 9^1 = 9 $
- $ 9^2 = 81 $

✔ So, $ 9^2 = 81 $ → Exponent = 2

---

5. $ 4^\square = 16 $

$ 4 = 2^2 $, so:
- $ 4^1 = 4 $
- $ 4^2 = 16 $

✔ So, $ 4^2 = 16 $ → Exponent = 2

---

6. $ 4^\square = 64 $

We already know:
- $ 4^1 = 4 $
- $ 4^2 = 16 $
- $ 4^3 = 64 $

✔ So, $ 4^3 = 64 $ → Exponent = 3

---

7. $ 16^\square = 256 $

Now, $ 16 = 2^4 $, so:
- $ 16^1 = 16 $
- $ 16^2 = 256 $

✔ So, $ 16^2 = 256 $ → Exponent = 2

---

Final Answers:

| Expression | Exponent |
|------------------|----------|
| $ 2^\square = 16 $ | 4 |
| $ 2^\square = 64 $ | 6 |
| $ 3^\square = 81 $ | 4 |
| $ 9^\square = 81 $ | 2 |
| $ 4^\square = 16 $ | 2 |
| $ 4^\square = 64 $ | 3 |
| $ 16^\square = 256 $ | 2 |

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✔ Answer Key:
1. 4
2. 6
3. 4
4. 2
5. 2
6. 3
7. 2

Let me know if you'd like a printable version or explanation with prime factorization!