Basic Algebra: One Step at a Time.  Pages 215 -226:   #109, 114, 115,  117, 118

Dr. Robert J. Rapalje

Seminole State College of Florida

Sanford, FL  32773

To see Section 2.13, with detailed explanations, examples, exercises, and answers, click here!

p. 225:   109.          

Solution:  There are two ways to simplify this problem. 

First method:   Notice that both the  and the  are raised to the  power.                

When you raise a power to a power, you multiply exponents:

                                or  

Second Method:  Work inside the parentheses first!  Observe that in the expression , the  exponent does NOT apply to the . 

Therefore,       .

Now,               

Finally, remember that when you raise a fraction to a negative 2 power, you must invert and square the fraction.

So, invert:       

And square:    

Final Answer:   

114.                         

Solution:   Again, there are two methods.  You can begin by working within the parentheses.  When you divide with the same base number, you subtract exponents:

Now, when you raise a power to a power, you multiply the exponents:

As a second method, you might want to raise the powers to powers (by multiplying exponents!) first.

Now, when you divide, you subtract exponents:

Final Answer:   

115.                        

Solution:  When you multiply with the same base number, you add exponents:

When you divide, you subtract exponents:

Final Answer:   

117.                         

Solution:  When you multiply with the same base number, you add exponents:

A quantity divided by itself is , so this is the final answer! 

OR--  You can say when  you divide with the same base number, you subtract exponents:

Final Answer:       (Since any nonzero number raised to the zero power is ).

118.                         

Solution:  When you multiply with the same base number, you add exponents:

When  you divide with the same base number, you subtract exponents:

Eliminate the negative exponent:

Final Answer: