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 |
---
✔ 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!
Parent Tip: Review the logic above to help your child master the concept of exponents math worksheet.