Manipulating fractional exponents

The  exercise appears under the Algebra I Math Mission. This exercise has several opportunities to manipulate and better understand fractional exponents.

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


 * 1) Simplify into a single exponent: This problem has a quotient or product that has a common base. The student is expected to rewrite the expression as a single exponential expression.Mfe1.png
 * 2) Find the error in the work: This problem provides a step-by-step worked out solution to an exponent simplification problem. The student is expected to find the step where an error in reasoning occurred.Mfe2.png
 * 3) Select all equivalent forms: This problem provides a particular exponential expression. The student is asked to select all of the expressions that are equivalent from a multiple select list.Mfe3.png

Strategies
Knowledge of the exponent rules and an ability to perform operations on rational numbers will ensure success on this exercise.
 * 1) With same bases, multiply turns to add, divide turns to subtract and powers are multiplication.
 * 2) Additionally, negative means to find the reciprocal and denominators are radicals.
 * 3) The Find the error in the work problems recycle often.

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."