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.