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Let's go through the questions one by one and solve them.

### 1. Hasil dari \( (2^4)^3 \cdot (2^2)^3 = \)
This is a multiplication of powers. Simplifying each term:
\[
(2^4)^3 = 2^{12}, \quad (2^2)^3 = 2^6
\]
Now, multiplying these:
\[
2^{12} \cdot 2^6 = 2^{12+6} = 2^{18}
\]

### 2a. Bentuk sederhana dari \( 2\sqrt{3} + 3\sqrt{12} = \)
First, simplify \( \sqrt{12} \):
\[
\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}
\]
Thus, the expression becomes:
\[
2\sqrt{3} + 3 \times 2\sqrt{3} = 2\sqrt{3} + 6\sqrt{3} = 8\sqrt{3}
\]

### 2b. Bentuk rasional dari \( \frac{6}{\sqrt{8} + \sqrt{5}} \) adalah
To rationalize the denominator, multiply by the conjugate:
\[
\frac{6}{\sqrt{8} + \sqrt{5}} \times \frac{\sqrt{8} - \sqrt{5}}{\sqrt{8} - \sqrt{5}} = \frac{6(\sqrt{8} - \sqrt{5})}{(\sqrt{8})^2 - (\sqrt{5})^2}
\]
Simplifying:
\[
= \frac{6(\sqrt{8} - \sqrt{5})}{8 - 5} = \frac{6(\sqrt{8} - \sqrt{5})}{3} = 2(\sqrt{8} - \sqrt{5})
\]
Now, simplify \( \sqrt{8} \):
\[
2(\sqrt{8} - \sqrt{5}) = 2(2\sqrt{2} - \sqrt{5}) = 4\sqrt{2} - 2\sqrt{5}
\]

### 3. Hasil dari \( (x^6)^4 \) adalah
Apply the power rule:
\[
(x^6)^4 = x^{6 \times 4} = x^{24}
\]

### 4. \( (\sqrt{9} + \sqrt{4})(\sqrt{9} - \sqrt{4}) = \)
This is a difference of squares:
\[
(\sqrt{9})^2 - (\sqrt{4})^2 = 9 - 4 = 5
\]

### 5. Jika \( a = 4 \) dan \( b = 5 \), maka nilai dari \( \frac{a^5(a^{-2}b)}{(ab)^2} \) adalah
First, expand both terms:
\[
\text{Numerator: } a^5 a^{-2} b = a^{5 - 2} b = a^3 b = 4^3 \times 5 = 64 \times 5 = 320
\]
\[
\text{Denominator: } (ab)^2 = (4 \times 5)^2 = 20^2 = 400
\]
Thus, the expression simplifies to:
\[
\frac{320}{400} = 0.8
\]

### 6. Bentuk sederhana dari \( \frac{6a^9 b^5 c^2}{2a^3 b^2 c^{-1}} \) adalah
Simplify the coefficients and each variable:
\[
= \frac{6}{2} \cdot a^{9-3} \cdot b^{5-2} \cdot c^{2 - (-1)} = 3a^6 b^3 c^3
\]

### 7. Nilai dari \( 2\sqrt{20} + \sqrt{50} = \)
First, simplify \( \sqrt{20} \) and \( \sqrt{50} \):
\[
\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}, \quad \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}
\]
Thus, the expression becomes:
\[
2 \times 2\sqrt{5} + 5\sqrt{2} = 4\sqrt{5} + 5\sqrt{2}
\]

### 8. Bentuk rasional dari \( \frac{5}{\sqrt{11} + 6} \) adalah
To rationalize the denominator, multiply by the conjugate:
\[
\frac{5}{\sqrt{11} + 6} \times \frac{\sqrt{11} - 6}{\sqrt{11} - 6} = \frac{5(\sqrt{11} - 6)}{11 - 36} = \frac{5(\sqrt{11} - 6)}{-25} = -\frac{1}{5}(\sqrt{11} - 6)
\]
Thus, the result is:
\[
-\frac{\sqrt{11}}{5} + \frac{6}{5}
\]

### 9. Bentuk rasional dari \( \frac{10}{\sqrt{2}} \) adalah
Multiply by the conjugate:
\[
\frac{10}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{10\sqrt{2}}{2} = 5\sqrt{2}
\]

### 10. Bentuk rasional dari \( \frac{4\sqrt{3}}{\sqrt{2}} \) adalah
Multiply by the conjugate:
\[
\frac{4\sqrt{3}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{4\sqrt{6}}{2} = 2\sqrt{6}
\]

Would you like more details or solutions for the remaining questions? Here are some related questions for further practice:

1. How do you simplify the square root of a fraction?
2. What is the difference of squares formula?
3. How do you rationalize a denominator?
4. What are the rules for multiplying and dividing exponents?
5. How do you simplify expressions with negative exponents?

**Tip:** When rationalizing denominators, always look for the conjugate of the denominator to eliminate the square root.

A set of math problems involving exponent rules, rationalization of denominators, and simplifying radical expressions.

Solve various problems involving exponentiation, square roots, and rationalization of denominators. Learn key concepts such as exponent rules, the difference of squares, and radical simplification. Ideal for students in Grades 9-11.

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