Lesson Page

Math A

Exponents

 

 

Exponents are the mathematician's shorthand.

 

2 2 2 is the same as 23, since there are three 2's being multiplied together.

 

Likewise, 5 5 5 5 = 54,because there are four 5's being multiplied together.

 

When we multiply negative numbers together, we must use parentheses to switch to exponent notation.
(-3)(-3)(-3)(-3)(-3)(-3) = (-3)6

-36 means something different.  It says to multiply six 3's together, and then take the negative of that answer.

(-3)6 = 729, but

-36 = -729 so be
careful with negative signs !

 

In general, the format for using exponents is:

(base)exponent

where the exponent tells you how many of the base are being multiplied together.

 

Zero Exponents

Zero can also be used as an exponent.  When it does appear, the value of the expression is 1.  For example:

Base0

Value

20 =

1

(-6)0 =

1

40 =

1

-80 =

-1
80=1
then take the negative of that answer= -1

 

 

Negative Exponents

Negative numbers as exponents have a special meaning.  The rule is as follows:

basenegative exponent =

For example:

Negative Exponent

Positive Exponent

4-1=

7-3=

(-5)-2=

 

 

Exponents can be very useful for evaluating expressions, especially if you learn how to use your calculator to work with them.

For more information on exponents in polynomial expressions, see Section 3, Operations on the Math A homepage.

 

 


   Murray