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I can help with solving the problems from the image. Here's the breakdown of the questions from the uploaded photo:

### 1. Tentukan hasil dari operasi bilangan berpangkat berikut:
a. \( \frac{5^3 \cdot 5^{-2}}{5^2} \)

b. \( 3^5 \cdot 6^{-5} \)

### 2. Tentukan hasil dari operasi bentuk-bentuk akar berikut:
a. \( \sqrt{3} \cdot ( \sqrt{5 \cdot 6} + 4\sqrt{5} ) \)

### 3. Rasionalkan pembagian bentuk akar berikut:
a. \( \frac{2\sqrt{10}}{\sqrt{7} - \sqrt{5}} \)

b. \( \frac{\sqrt{5}}{\sqrt{8}} \)

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Let me start solving the problems one by one. 

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### Problem 1a: \( \frac{5^3 \cdot 5^{-2}}{5^2} \)
Using the exponent rule \( a^m \cdot a^n = a^{m+n} \), first simplify the numerator:
\[
5^3 \cdot 5^{-2} = 5^{3 - 2} = 5^1 = 5
\]
Now, divide by \( 5^2 \):
\[
\frac{5}{5^2} = 5^{1 - 2} = 5^{-1} = \frac{1}{5}
\]

### Problem 1b: \( 3^5 \cdot 6^{-5} \)
Here, you cannot simplify directly because the bases are different. The expression will remain as:
\[
3^5 \cdot 6^{-5} = \frac{3^5}{6^5}
\]
This can be written as:
\[
\left( \frac{3}{6} \right)^5 = \left( \frac{1}{2} \right)^5 = \frac{1}{32}
\]

### Problem 2a: \( \sqrt{3} \cdot \left( \sqrt{5 \cdot 6} + 4 \sqrt{5} \right) \)
First, simplify the terms inside the parentheses:
\[
\sqrt{5 \cdot 6} = \sqrt{30}
\]
So the expression becomes:
\[
\sqrt{3} \cdot \left( \sqrt{30} + 4 \sqrt{5} \right)
\]
Distribute \( \sqrt{3} \) to both terms:
\[
\sqrt{3} \cdot \sqrt{30} = \sqrt{90}, \quad \sqrt{3} \cdot 4 \sqrt{5} = 4 \sqrt{15}
\]
Thus, the final answer is:
\[
\sqrt{90} + 4 \sqrt{15}
\]
Since \( \sqrt{90} = 3 \sqrt{10} \), the final simplified expression is:
\[
3 \sqrt{10} + 4 \sqrt{15}
\]

### Problem 3a: \( \frac{2 \sqrt{10}}{\sqrt{7} - \sqrt{5}} \)
To rationalize this, multiply both numerator and denominator by the conjugate of the denominator:
\[
\frac{2 \sqrt{10}}{\sqrt{7} - \sqrt{5}} \cdot \frac{\sqrt{7} + \sqrt{5}}{\sqrt{7} + \sqrt{5}} = \frac{2 \sqrt{10} (\sqrt{7} + \sqrt{5})}{(\sqrt{7})^2 - (\sqrt{5})^2}
\]
Simplify the denominator:
\[
(\sqrt{7})^2 - (\sqrt{5})^2 = 7 - 5 = 2
\]
So the expression becomes:
\[
\frac{2 \sqrt{10} (\sqrt{7} + \sqrt{5})}{2}
\]
Cancel the 2:
\[
\sqrt{10} (\sqrt{7} + \sqrt{5}) = \sqrt{70} + \sqrt{50}
\]
Thus, the final answer is:
\[
\sqrt{70} + 5 \sqrt{2}
\]

### Problem 3b: \( \frac{\sqrt{5}}{\sqrt{8}} \)
Simplify the square roots:
\[
\frac{\sqrt{5}}{\sqrt{8}} = \frac{\sqrt{5}}{2\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{10}}{4}
\]

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If you'd like me to further explain or if you have any questions, let me know!

Here are 5 related questions:
1. What are the rules for multiplying and dividing powers with the same base?
2. How do you simplify radical expressions involving multiplication?
3. What is the process for rationalizing denominators with radicals?
4. How can you simplify expressions involving the product of different square roots?
5. Why does multiplying by the conjugate help in rationalizing denominators?

**Tip:** When working with radicals, always check if the radical can be simplified further before performing operations!

Tentukan hasil dari operasi bilangan berpangkat dan bentuk-bentuk akar pada Ulangan Harian kelas 10.

Pelajari cara menyelesaikan operasi bilangan berpangkat dan bentuk-bentuk akar pada soal Ulangan Harian kelas 10, dengan penjelasan langkah-langkah rinci. Materi mencakup konsep eksponen, radikal, dan rasionalisasi bentuk akar. Cocok untuk siswa kelas 10.

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