Exponents
When the same number is multiplied by itself, the indicated product can be
written inexponential notation. For example, 33 can be written as 3^2 ; there
the 3 is called thebaseand the 2 is called theexponent. Also,
3 3 3 ¼ 33
3 3 3 3 ¼ 34
3 3 3 3 3 ¼ 35 ;etc.
32 is read as ‘‘three squared’’ or ‘‘three to the second power,’’ 3^3 is read as
‘‘three cubed’’ or ‘‘three to the third power,’’ 3^4 is read as ‘‘three to the fourth
power,’’ etc.
Math Note: When no exponent is written with a number, it is
assumed to be one. For example, 3¼ 31.EXAMPLE
Find 5^3.
SOLUTION
53 ¼ 5 5 5 ¼ 125
EXAMPLE
Find 2^8.
SOLUTION
28 ¼ 2 2 2 2 2 2 2 2 ¼ 256
Exponents can be used with negative numbers as well. For example,ð 8 Þ^3
meansð 8 Þð 8 Þð 8 Þ. Notice that in the case of negative numbers, the
integer must be enclosed in parentheses. When thesign isnotenclosed in
parentheses, it isnotraised to the power. For example, 83 means 8 8 8.
EXAMPLE
Findð 5 Þ^4.
CHAPTER 2 Integers 31