Rational exponents are exponents that are expressed as fractions. They are an important concept in algebra as they involve both roots and powers. Teaching rational exponents to students can be a challenge, but it is one that is essential to their understanding of algebraic operations. There are many activities that can help students to learn operations with rational exponents.

**1. Introduction to rational exponents:**

Start by introducing rational exponents to students with a brief explanation. Explain the difference between rational and irrational numbers and provide examples. Use diagrams to illustrate rational exponents.

**2. Simplifying rational exponents:**

Teach students how to simplify rational exponents by simplifying them to second power, which is equal to the square root. Use a chart or table to show how the exponent simplifies.

**3. Multiplying rational exponents:**

Show students how to multiply rational exponents. Highlight the fact that when the bases are the same, we simply add the exponents to get the product.

**4. Dividing rational exponents:**

Teach students how to divide rational exponents using the same method used to multiply them. Highlight the rules of exponents, which states that we subtract the exponents when dividing expressions with the same base.

**5. Roots of rational exponents:**

Once students understand exponents and fractional exponents they can learn roots of exponents. Explain the meaning and the methods of obtaining different roots of a rational exponent.

**6. Positive and negative rational exponents:**

Lastly, teach students how to calculate positive and negative rational exponents. Discuss the difference between positive and negative exponents and the relationship between the two.

Incorporate various activities into your instruction to help teach students rational exponents. Some of these activities could include creating math games that require students to use rational exponents, working on real-world problem-solving activities, and group activities where students can work out problems together. Emphasize real-life applications of rational exponents, such as simplifying measurements and calculating growth rates.

In conclusion, teaching operations with rational exponents is not always easy, but with the right activities, it can be an engaging and exciting experience for students. Introduce rational exponents step by step, using real-world examples to make the concept more accessible. When students can relate to mathematical concepts, they are more engaged, and this results in improved overall subject understanding.