Multi-step simplification of rational exponent expressions

The  exercise appears under the Algebra I Math Mission. This exercise practices evaluating numerical expressions and simplify variable expressions with mixed exponential and radical terms, by using the properties of exponents.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the value of the variable: This problem has a numerical expression involving a rational expression with multiple exponents and radicals with fractions and variables. Some of the variables are constants. Some also may be negative. The student is expected to find the value of one of the variables and type it in the text box below. Multi-step simplification of rational exponent expressions.PNG

Strategies
Knowledge of the exponent rules and solving radicals, including negative and fraction values, are 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."