# Algebra

**Question description**

Simplify
each expression using the rules of exponents and examine the steps
you are taking. Your post must be a minimum of 250 words.

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

*n*th root

*Use the rules of exponents to simplify the expression.*

*1. *

*Simplify the expression. Write your answers with positive exponents. Assume that all variables represent positive real numbers.*

*2. *

Refer
to Inserting
Math Symbols 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.

Your
initial post should be at least 250 words in length. Support your
claims with examples from required material(s) and/or other scholarly
resources, and properly cite any references.

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