Let's go through the questions from the image:

1. Bilangan berpangkat untuk 0.0001 adalah ....

This is asking for the exponential form of 0.0001. $0.0001 = 10^{-4}$ Answer: b. $10^{-4}$

2. Nilai $\text{yang memenuhi } \frac{(-2)^3 \cdot (2^2)^{-1}}{-2 \times (3)^{-3}} \text{ adalah ....}$

We need to simplify the expression step by step.

• Numerator: $(-2)^3 = -8$ and $(2^2)^{-1} = \frac{1}{4}$ Thus, numerator = $\frac{-8}{4} = -2$.

• Denominator: $-2 \times (3)^{-3} = -2 \times \frac{1}{27} = -\frac{2}{27}$.

Thus the full expression becomes: $\frac{-2}{-\frac{2}{27}} = 27$ Answer: a. $27$

3. Nilai dari $\left( \frac{2}{3} \right)^2 \div \left( -\frac{3}{15} \right)^2 \text{ adalah ....}$

• $\left( \frac{2}{3} \right)^2 = \frac{4}{9}$
• $\left( -\frac{3}{15} \right)^2 = \left( -\frac{1}{5} \right)^2 = \frac{1}{25}$

Now, the division: $\frac{4}{9} \div \frac{1}{25} = \frac{4}{9} \times \frac{25}{1} = \frac{100}{9}$ Answer: b. $\frac{100}{9}$

4. Nilai dari $(-2)^3 \times 2^3 \div \frac{2}{3} \text{ adalah ....}$

• $(-2)^3 = -8$
• $2^3 = 8$

So, $(-8) \times 8 = -64$ $-64 \div \frac{2}{3} = -64 \times \frac{3}{2} = -96$ Answer: None of the provided options seem to match.

5. Bentuk sederhana dari $\sqrt{2} + \sqrt{50} - \sqrt{12} \text{ adalah ....}$

Simplify each term: $\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}, \quad \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$ So, the expression becomes: $\sqrt{2} + 5\sqrt{2} - 2\sqrt{3} = 6\sqrt{2} - 2\sqrt{3}$ None of the provided options exactly match this form. Therefore, there might be an error in the options.

Do you want details for any specific question or need further clarification?

5 Related Questions:

1. How do you simplify exponents with negative bases?
2. What are the rules for dividing fractions?
3. How do you simplify radical expressions?
4. Can you show another example of converting a decimal to an exponent?
5. How do you handle negative exponents in equations?

Tip:

Always break down complex expressions into smaller steps and deal with powers, roots, and fractions separately before combining them back together!