Simplifying Expressions Involving VariablesSimplify each expression. Assume the variables represent any real numbers and use absolute value as necessary. See Example 8.

In this discussion, you will simplify and compare equivalent expressions written both in radical form and with rational (fractional) exponents.

Simplify each expression using the rules of exponents and examine the steps you are taking.

Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing. Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work.

Principal root

Product rule

Quotient rule

• Reciprocal

nth root

• Refer to Inserting Math Symbols Download  for guidance with formatting. Be aware with regards to the square root symbol, you will notice that it only shows the front part of a radical and not the top bar. Thus, it is impossible to tell how much of an expression is included in the radical itself unless you use parenthesis. For example, if we have ?12 + 9 it is not enough for us to know if the 9 is under the radical with the 12 or not.  Therefore, we must specify whether we mean it to say ?(12) + 9  or  ?(12 + 9), as there is a big difference between the two. This distinction is important in your notation.

Another solution is to type the letters “sqrt” in place of the radical and use parenthesis to indicate how much is included in the radical as described in the second method above. The example above would appear as either “sqrt(12) + 9” or  “sqrt(12 + 9)” depending on what we needed it to say.