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1. **Hasil dari (-1)^9 + (1/2)^(-1) = ...**
   - \((-1)^9 = -1\) because the exponent is odd.
   - \((1/2)^{-1} = 2\) because taking the reciprocal of \(1/2\) gives 2.
   - Therefore, \((-1)^9 + (1/2)^{-1} = -1 + 2 = 1\).

   **Answer: 1**

2. **Hasil dari \(\left[\frac{2}{3}\right]^{-2}\) adalah = ...**
   - \(\left(\frac{2}{3}\right)^{-2}\) means the reciprocal squared.
   - Reciprocal of \(\frac{2}{3}\) is \(\frac{3}{2}\), and squaring it gives \(\frac{9}{4}\).

   **Answer: \(\frac{9}{4}\)**

3. **Bentuk sederhana dari \((2^4)^2 \times \left(\frac{1}{2}\right)^{-2} = ...**
   - \((2^4)^2 = 2^{8}\).
   - \(\left(\frac{1}{2}\right)^{-2} = 2^2\) because of the negative exponent.
   - Therefore, \(2^8 \times 2^2 = 2^{10} = 1024\).

   **Answer: 1024**

4. **Hasil dari \(81^{\frac{1}{4}} - 125^{\frac{1}{3}} + 4^{\frac{3}{2}} = ...**
   - \(81^{\frac{1}{4}} = \sqrt[4]{81} = 3\).
   - \(125^{\frac{1}{3}} = \sqrt[3]{125} = 5\).
   - \(4^{\frac{3}{2}} = \sqrt{4}^3 = 2^3 = 8\).
   - Therefore, \(3 - 5 + 8 = 6\).

   **Answer: 6**

5. **Hasil dari \(0^5 + (-3)^0 = ...**
   - \(0^5 = 0\) because any number raised to a power is 0.
   - \((-3)^0 = 1\) because any number raised to 0 is 1.
   - Therefore, \(0 + 1 = 1\).

   **Answer: 1**

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Would you like further clarification or a breakdown of any of the steps? Here are five related questions for practice:

1. What is the value of \( (-2)^3 + (4/5)^{-1} \)?
2. Simplify \( (3/4)^{-3} \).
3. Evaluate \( (5^3)^2 \times (1/3)^{-3} \).
4. Find the result of \( 16^{1/2} - 64^{1/3} + 9^{3/2} \).
5. What is the sum of \( 2^0 + (-1)^0 \)?

**Tip:** When working with exponents, always remember that negative exponents indicate a reciprocal, and fractional exponents relate to roots!

Solve the following mathematical problems: 1. (-1)^9 + (1/2)^(-1), 2. [2/3]^-2, 3. (2^4)^2 * (1/2)^(-2), 4. 81^(1/4) - 125^(1/3) + 4^(3/2), 5. 0^5 + (-3)^0

Learn how to solve exponent and root problems including powers of negative numbers, fractional exponents, and the properties of zero and negative exponents. This guide covers step-by-step solutions to problems such as (-1)^9 + (1/2)^(-1) and more. Ideal for high school students.

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