Test your skills on the following problems:
1. 
Rewrite
the following expression without using
exponents: 8^{4} 


2. 
Which
of the following is equal to the expression:
3^{7} 
Choose
one:


3. 
What
is the value of the expression:
(2)^{3}(3)^{2
}? 



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



5. 
The
expression (3^{0})(4^{0})(2^{2})
is equal to: 



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 (10^{0}), tens (10^{1}),
hundreds (10^{2}), thousands (10^{3})
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.)
______
______ ______ ______
______ ______ ______
______
2^{7
} 2^{6}
2^{5}
2^{4}
2^{3}
2^{2}
2^{1}
2^{0}

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)?

