Understanding fractional exponents

The  exercise appears under the Algebra I Math Mission. This exercise explores the meaning of rational exponents.

Types of Problems
There are two types of problems in this exercise:


 * 1) Fill in the values to find the exponent: This problem provides three blanks that can be used to understand the relationship between radicals and fraction exponents. The student is asked to fill in the value of the first two numerical expressions, and then use these values to infer the correct exponent to represent a radical.Ufe1.png
 * 2) Give the correct exponent: This problem presents a radical expression. The student is asked to give the correct rational exponent that would represent the radical expression.Ufe2.png

Strategies
Knowledge of beginning exponent rules can be used to understand this exercise, but knowing the advanced exponent rules would ensure accuracy and efficiency.
 * 1) Generally $$a^{(\frac{1}{n})}$$ is the nth root of a.
 * 2) on the Fill in the values to find the exponent problem, the first two answers are the same, and they are the number under the radical, or in the base of the exponent. The final answer is the fraction that is formed by one over the index of the radical.
 * 3) On the Give the correct exponent problem, the answer is the fraction formed by the taking the exponent on the number in the radical over the index of the radical.

Real-life Applications

 * 1) Fractional exponents are very useful in calculus because the power rule for taking derivatives and integrals is much simpler than the typical limit definition.