Practice with
 Exponents
 Topic Index | Algebra Index | Regents Exam Prep Center


Test your skills on the following problems:

1.

Rewrite the following expression without using exponents:    84

 

 

 

2. Which of the following is equal to the expression:    
                                       3-7
Choose one:

37
(-3)7

 

 

3. What is the value of the expression:
                                 (-2)3(3)2 ?

-72
   72
 -36

 

 

4. Which of the following has a value of 1 ?

(-1)2
 1-1
 10
 all of the above

 

5. The expression  (30)(40)(22) is equal to:
4
 1
 0
 none of the above

 
 

Now let's investigate a situation involving exponents:

6. Computers store information with electrical components that are either "on" or "off".  Each component stores a bit, which has a value of either 1 (on) or 0 (off).  Such a process uses the binary number system, or the base 2 number system.  Remember that our decimal system (base 10) represents numbers as powers of ten:
                    units (100), tens (101), hundreds (102), thousands (103) and so on.
The binary system works in the same way with a base value of 2.
a.  What is the value represented by each place in a binary number?  (Fill in the blanks.)

      ______    ______   ______   ______   ______   ______   ______   ______ 
         27              26           25          24           23          22          21           20       

b.  What is the decimal value of the binary number  10111 ?  (If a 1 appears, you are to add the value of that place holding to the total value of the number.)
c.   Eight bits, as shown in part a, comprise a byte.  If all of the bits in a byte were "turned on" (1), what is the largest decimal value that can be stored in one byte (8 bits)?