Exponential Expressions MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts
 An exponential expression is one which contains an exponent.

When working with exponential expressions, you will need to remember the rules that pertain to dealing with exponents. Algebra 2 will expect you to use these rules (forward and backward) in a variety of situations. Primarily, you will need to remember the following rules:

 Product Rule: Quotient Rule: Power to Power Rule: Product to Power Rule:

 Simplifying Exponential Expressions:

Simplify the following expressions into the form a•bx.
 1 Solution: Rule: 2 Solution: Rule: 3 Solution:  Get a common base. Rule: Rule: 4 Solution: Get a common base. Rule: Rule: 5 Solution: Simplify 2nd term. Rule: Rule: 6 Solution:   Simplify quotient. Rule: Rule: Rule:

 Re-writing Exponential Expressions:

You may be asked to re-write an exponential expression in a simpler form, as seen above, to make it more easily readable. Or you may be asked to re-write the expression into a more obscure form to reveal pertinent information about a concept or about the expression itself.
 1 Find K. Solution:   Let's see if we can re-write the left-hand side to contain an exponent of simply x. Better, but not good enough. If we cannot simplify the left-side further, how can we manipulate what we have into becoming K x ? 2 To rewrite , A will be _____. Solution:    We need the exponent on 4 to contain a 3. We can introduce 3•1/3 (which equals 1) without changing the expression. 3 Find M, such that Solution:   Separate the exponent to produce the x alone. 4 Find B. Solution:  Re-write the first term and then factor. 5 Find a and b: Solution: Yikes! Let's work on that exponent first.    OK, so far, so good. Now, work on the -1 by adding a 0 as -1+1. a = 2 and b = 4

 NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation and is not considered "fair use" for educators. Please read the "Terms of Use".