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Exponent Rules
Contributed by: Miles
(Original author: Maccoux)

To multiply exponents with the same base, 

ADD the powers 

x*x

x2 • x3 =

•
x*x*x =     x*x*x*x*x
x2+3 = x5

To multiply exponents, ADD powers

x • x3 =

x
•
x*x*x =    x*x*x*x
x1+3 = x

To multiply exponents, ADD powers

x5 • x3 =

x

x•x5•x3 =

To multiply exponents, ADD powers

x1+5+3 = x

To multiply exponents, ADD powers

x2•x5•x-3 =

x

To multiply exponents, ADD powers

x-5 • x-6 = 

x

x5 • x-3 =

To multiply exponents, ADD powers

x5+-3 = x

To raise a power to another power,

         MULTIPLY powers

(x5)3 =

x5*3 = x

To raise a power to another power,

         MULTIPLY powers

(x5)6 =

x

To raise a power to another power,

         MULTIPLY powers

(x3)6 =

x

(x5y3)7 =

To raise several powers to

another power, MULTIPLY ALL

(inside) powers by the outside power.

  x5*7y3*7= x   y

To raise several powers to

another power, MULTIPLY ALL

(inside) powers by the outside power.

(x5y3)  = 

8
x    y
To divide exponents, SUBTRACT powers

 

x3
x2
   numerator
- denominator
=
x      =
3 - 2
x
To divide exponents, SUBTRACT powers

 

   numerator - denominator
x2
x7
=
x
To divide exponents, SUBTRACT powers

 

   numerator - denominator
x5
x8
=
x
To divide exponents, SUBTRACT powers

 

x3
x3
   numerator
- denominator
=
x
Whole number
=
To divide exponents, SUBTRACT powers

 

   numerator - denominator
x2y4
x8y7
=x   y

                      Parentheses first

(raise both powers (2 and 4) to the 3rd power)

x   y

(x2y4)3•x5 

•x5
= x    y 
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