https://file.aiquickdraw.com/mathbot/file/17302255373851grso3lv.jpg

Let's go through each of the problems quickly using the rule given:  
\[
a^{\frac{1}{n}} = \sqrt[n]{a}
\]

### Solution Steps:
1. **Problem 1: \( 4^{\frac{1}{2}} \)**
   - This expression represents the square root of 4.
   - \( \sqrt{4} = 2 \)
   - **Answer:** \( 4^{\frac{1}{2}} = 2 \)

2. **Problem 2: \( 8^{\frac{1}{3}} \)**
   - This expression represents the cube root of 8.
   - \( \sqrt[3]{8} = 2 \)
   - **Answer:** \( 8^{\frac{1}{3}} = 2 \)

3. **Problem 3: \( (-27)^{\frac{1}{3}} \)**
   - This expression represents the cube root of -27.
   - \( \sqrt[3]{-27} = -3 \)
   - **Answer:** \( (-27)^{\frac{1}{3}} = -3 \)

These solutions follow the definition given in the instructions. Let me know if you'd like additional details or have any questions.

### Related Questions:
1. How can we simplify expressions with exponents greater than 1, like \( a^{\frac{m}{n}} \)?
2. What are the rules

Solve the expressions involving fractional exponents by converting to radical notation and simplifying.

Learn how to simplify expressions with fractional exponents by converting them to radical notation. This step-by-step solution demonstrates how to solve expressions like 4^(1/2), 8^(1/3), and (-27)^(1/3) using the definition of fractional exponents. Ideal for high school students in Grades 9-10.

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