Learning Objectives
Introduction
This tutorial picks up where Tutorial 23: Exponents and Scientific Notation Part I left off. It finishes the rules of exponents with raising a base to two exponents, raising a product to an exponent and raising a quotient to an exponent. Also we will revisit the concept of scientific notation. Like it or not, the best way to master these exponents is to work through exponent problems. So I guess we better get to it.
Tutorial
Note how 2 times 3 is 6, which is the exponent of the final answer. We can think of this as 3 groups of 2, which of course would come out to be 6.
Base Raised to two ExponentsAgain, you can think of it as n groups of m if it helps you to remember.
Example 1: Simplify .
Note how both bases of your product ended up being raised by the exponent of 3.
A Product Raised to an ExponentExample 2: Simplify .
Since, division is really multiplication of the reciprocal, it has the same basic idea as when we raised a product to an exponent.
A Quotient Raised to an ExponentExample 3: Simplify .
*When raising a quotient to an exponent, raise each base of the quotient to that exponent
*Use def. of exponents to evaluate
*Rewrite
with a pos. exp. by taking recip. of base
*Raise each
base to 10
*Mult.
your exponents
*Rewrite with a pos. exp. by taking recip. of base
*When
div. like bases you sub. your exp.
Practice Problems
To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer.
Practice Problems 1a - 1c: Simplify, use positive exponents to write each answer.
Practice Problems 2a - 2b: Perform indicated operations, write each result in scientific notation.
Need Extra Help on these Topics?
http://www.sosmath.com/algebra/logs/log3/log33/log33.html
This webpage helps with the rule for raising a base to two
exponents.
http://www.purplemath.com/modules/exponent.htm
This webpage gives an overall review of exponents. It contains
rules from both this tutorial and Tutorial 23: Exponents and Scientific
Notation Part I.
http://www.ltcconline.net/greenl/courses/152A/polyExp/intexp.htm
This webpage gives an overall review of exponents. It contains
rules from both this tutorial and Tutorial 23: Exponents and Scientific
Notation Part I.
Go to Get Help Outside the Classroom found in Tutorial 1: How to Succeed in a Math Class for some more suggestions.
Last revised on July 12, 2011 by Kim Seward.
All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward. All rights reserved.