Download Negative Exponents

Negative Exponents
If a is a real number other than 0 and n is a positive integer, then
an 
1
an
In layman’s terms, this means that any real number or variable that contains a negative
exponent, you flip the number. Don’t complicate this! Once you move a negative
exponent to its opposite place (meaning numerator and denominator), the negative
exponents become positive.
Examples:
52 
1
1

2
5
25
(4)4 
2x 3 
1
1

(4)4 256
2
x3
(3x)1 
Never leave a number with an exponent. Figure it out!
1
3x
Be careful with numbers in parentheses. I negative
exponent outside parentheses is applied to everything
in the parentheses.
In this problem, the exponent is applied only to the x variable and not
the 2. Move only the variable.
In this problem, the negative exponent belongs to everything inside
parentheses. Move the entire term to the denominator.
m5
1
515
10

m

m

m15
m10
21  32 
For this problem, we follow the rules for exponents by
subtracting the exponents and always making sure
that the answer has only positive exponents.
1 1 1 1 9 2 11
     
2 32 2 9 18 18 18
For the above problem, you first need to move the numbers so you have positive
exponents. Next, figure out the exponent. Remember that when adding or subtracting
fractions you always need to have a common denominator.
x 9
1
1


x 2 x 2 x9 x11
First, move the x-9 to the bottom to make it positive. Then follow the
rules for exponents when multiplying to get the answer.
5 p4
 5 p 4 p3  5 p 7
3
p
In this problem, we need to bring up the p-3 to make it positive
in the numerator and then follow the rules for exponents.
23 2 2 1
  
21 23 8 4
Both exponents are negative so they get moved. Simplify the 23
and remember to reduce your answer if possible.
2 x 7 y 2 2 y 2 y 5 y 7


10 xy 5 10 xx7 5 x8
(3x 3 )( x 2 ) 3x 2 3x 2 3
 3 6 9  7
x6
xx
x
x
Do not do these problems in your head. Write them
down. Move all negative exponents to make them
positive first and then combine like terms following
the rules of exponents.