1.07  Laws of Exponents

Intermediate Algebra: One Step at a Time,    Pages  90 - 95:   #35, 37, 40, 43, 51, Extra Problem

Dr. Robert J. Rapalje

Seminole State College of Florida

Sanford, FL  32773

To see Section 1.07, with explanations, examples, exercises, and answers, click here!

NOTE:  If the Laws of Exponents "Quickies" problems are beating you up, then maybe you could use some additional explanation. 

            Try these links from Basic Algebra: One Step at a Time:

P. 93  # 35.                   

Solution:

The base number for each of these factors is x.  Remember that when you multiply with the same base number, you put down the base number and you add exponents: 

Now, a number divided by itself is 1, so the final answer is 1.  However, if you wanted to do so, you could also remember that when you divide with the same base number, you put down the base number and subtract exponents: 

P. 93 # 37.     

Solution: 

Notice that in this exercise, you have products within parentheses raised to a power.  The  basic law of exponents that applies here is that when you raise a power to a power, you MULTIPLY the exponents.

Next, you know that when you multiply with the same base number, you ADD the exponents: 

To eliminate a negative exponent, remember that , so the final answer is

                          or  

p. 94  # 40.                   

Solution:

Notice that in this exercise, you have products within parentheses raised to a power.  The  basic law of exponents that applies here is that when you raise a power to a power, you must put down the base number and multiply the exponents.

Next, you know that when you multiply with the same base number, you put down the base number and you add exponents:   and

To eliminate a negative exponent, remember that , so the final answer is

                          or  

P. 94  # 43.               

Solution:

Notice that in this exercise, you have a quotient whose numerator and denominator contain products within parentheses raised to a power.  The  basic law of exponents that applies here is that when you raise a power to a power, you must put down the base number and multiply the exponents.

This fraction can actually be rewritten as three separate fractions:

Next, you know that when you divide with the same base number, you put down the base number and subtract the exponents:

To eliminate a negative exponent, remember that   and , so the final answer is

                          or  

P. 95  # 51.        

Solution:

The base number for each of these factors is x.  Remember that when you multiply with the same base number, you put down the base number and you add exponents: 

Next, remember that when you divide with the same base number, you put down the base number and subtract exponents: 

                       

Extra Problem from Dave in Australia:     

Solution:

The base number for each of these factors is a.  First, I recommend that you multiply the 7 times 3, which is 21.  Remember that when you multiply with the same base number, you put down the base number and you add exponents.  This means that you add 2m plus –n, which is 2m-n. 

Next, divide out the 21 with the 42.  Also, remember that when you divide with the same base number, you put down the base number and subtract exponents: 

                          or     or   

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