Rational exponents can be difficult for students to understand and evaluate, particularly when it involves integers. However, with the right activities, students can learn to evaluate integers raised to rational exponents confidently.

Here are some activities that can help:

1. Fractional Powers Dominoes:

A fun way to teach students about fractional powers is to have them play a game of dominoes. In this game, half of each domino will have an integer (the base) and the other half will have a fraction (the exponent). Students must match the base and exponent, simplifying the expression and finding the value of the fraction.

2. Paper Folding:

Use paper folding to demonstrate the relationship between integers raised to rational exponents and square roots. Students can fold a piece of paper in half repeatedly and compare the result with multiplying or dividing by 2 raised to a fractional power. It helps them to make connections between different forms of expression.

3. Evaluate Fractions of Powers:

Give students a set of expressions that involve fractional powers and ask them to convert the fractional power to a radical. It can be a group or individual task wherein each group or student will present their solutions to the class. Also, have the students work on a few questions assessing their knowledge about perfect squares and perfect cubes.

4. The Process of Elimination:

Write a set of expressions on the board that contain fractional powers of integers. Students can then evaluate them systematically by cross-referencing the base and exponent with unlikely numerical expressions. It will assist them in eliminating answers that do not match the mathematical criteria used to evaluate them.

5. Group Discussions:

Students are divided into groups, each with a different expression to evaluate in terms of its fractional powers. Every student should discuss their work with one another and compare their solutions. They should also be encouraged to go over each other’s work and point out any oversights.

In conclusion, these activities can help construct a strong foundation for understanding the concept of evaluating integers raised to rational exponents. The skills and knowledge students learn in these exercises are all applicable to solving more complex expressions and can be easily transferred to other mathematical areas. Remember, when it comes to learning math, hard work plus effort leads to success!