Rational exponents and radicals

The  exercise appears under the Algebra I Math Mission. This exercise practices evaluating numerical expressions with rational exponents, and convert between equivalent forms of exponential and radical expressions.

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


 * 1) Find the value of the variable: This problem has a numerical expression involving a rational exponent with fractions and variables. One of the variables is a constant. The student is asked to find the value of one of the variables and type it in the text box below.  Rational exponents and radicals.PNG
 * 2) Determine the equivalent expression(s): This problem has a numerical expression involving a rational exponent with fractions. The student is asked to find the expression(s) (if any) that are equivalent the original and select it from the multiple choice list below. Rational exponents and radicals2.PNG

Strategies
Knowledge of the exponent rules, including negative and fraction values, is sufficient to perform the exercise accurately and efficiently.
 * 1) Negative exponents mean to reciprocate (or find the inverse/opposite), and a fraction like $$\frac{1}{n}$$ means to find the $$n\text{th}$$ root.
 * 2) The problems at this level tend to be a straight radical with no additional powers mixed in, although there is a possibility of needing to find the reciprocal of the answer.

Real-life Applications

 * 1) An ability to work well with exponents of all types is an advantage in calculus where derivatives can be made simpler via the "power rule."