Drag each tile to the correct box.

To evaluate the given expressions, we'll simplify them one by one.

1. **Expression: \( 2^{-2} \times 2^{-3} \)**
- Using the property of exponents: \( a^m \times a^n = a^{m+n} \)
- \( 2^{-2} \times 2^{-3} = 2^{-2 + (-3)} = 2^{-5} = \frac{1}{2^5} = \frac{1}{32} \)

2. **Expression: \( \frac{7^8}{7^8} \)**
- Any non-zero number divided by itself equals 1.
- \( \frac{7^8}{7^8} = 1 \)

3. **Expression: \( 4^2 \times 4^{-1} \)**
- Using the property of exponents: \( a^m \times a^n = a^{m+n} \)
- \( 4^2 \times 4^{-1} = 4^{2 + (-1)} = 4^{1} = 4 \)

4. **Expression: \( \frac{5^{-10}}{5^{-12}} \)**
- Using the property of exponents: \( \frac{a^m}{a^n} = a^{m-n} \)
- \( \frac{5^{-10}}{5^{-12}} = 5^{-10 - (-12)} = 5^{2} = 25 \)

Now we have evaluated each expression:
1. \( 2^{-2} \times 2^{-3} = \frac{1}{32} \)
2. \( \frac{7^8}{7^8} = 1 \)
3. \( 4^2 \times 4^{-1} = 4 \)
4. \( \frac{5^{-10}}{5^{-12}} = 25 \)

Next, we will list the values in order from greatest to least:
- **25**
- **4**
- **1**
- **\(\frac{1}{32}\)**

Now let's write them in order according to the expressions:
- \( \frac{5^{-10}}{5^{-12}} \) (25)
- \( 4^2 \times 4^{-1} \) (4)
- \( \frac{7^8}{7^8} \) (1)
- \( 2^{-2} \times 2^{-3} \) (\(\frac{1}{32}\))

So the final order from greatest to least is:
1. \( \frac{5^{-10}}{5^{-12}} \)
2. \( 4^2 \times 4^{-1} \)
3. \( \frac{7^8}{7^8} \)
4. \( 2^{-2} \times 2^{-3} \)