Equivalent forms of exponential expressions

The  exercise appears under the Algebra I Math Mission. This exercise practices exponent rules by rewriting exponential expressions.

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


 * 1) Find the value of the coefficient and base: This problem provides an exponential expression. The student is asked to manipulate the given expression into one with a very specific form and provide the coefficient and the base in the space provided.Efoee1.png
 * 2) Select equivalent expressions: This problem provides an exponential expression and various other expressions that may or may not be the same in a multiple select list. The student is expected to find the expressions that are the same.Efoee2.png

Strategies
Knowledge of exponent rules will ensure success on this exercise.
 * 1) The expression given in Find the value of the coefficient and base will work out but will sometimes require strategic manipulation. To ensure accuracy, break into the smallest prime bases possible and expand and combine as needed.
 * 2) Equivalent exponential expressions can be located by evaluating the expressions at some fixed value. Unfortunately, this technique is necessary but not sufficient, so it may yield additional incorrect expressions.

Real-life Applications

 * 1) In second semester calculus it is discovered that polynomials can be used to represent most functions in convenient ways (for example, Taylor's series). Comfort with exponent rules is a pre-skill to get to this point.