""Final Exponent Rules

To multiply exponents, ADD 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 =

x5+3 = x

x•x5•x3 =

To multiply exponents, ADD powers

x1+5+3 = x

x2•x5•x-3 =

To multiply exponents, ADD powers

x2+5+-3 = x

x-5 • x-6 =

To multiply exponents, ADD powers

x-5+-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 =

x5*6 = x

To raise a power to another power,

         MULTIPLY powers

(x3)6 =

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

(x5y3)8 =

To raise several powers to

another power, MULTIPLY ALL

(inside) powers by the outside power.

x5*8y3*8 = x    y

(xy6)7 =

To raise several powers to

another power, MULTIPLY ALL

(inside) powers by the outside power.

x1*7y6*7 = x    y
To divide exponents, SUBTRACT powers

 

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

 

x2
x7
=
   numerator
- denominator
x7-2 =
x
To divide exponents, SUBTRACT powers

 

x5
x8
=
   numerator
- denominator
x8-5 =
x
To divide exponents, SUBTRACT powers

 

x3
x3
=
   numerator
- denominator
x3-3 =
x
Whole number
=
To divide exponents, SUBTRACT powers

 

x8y7
x2y4
=
x8-2•y7-4
   numerator
- denominator
=x   y

                      Parentheses first

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

x   y

(x2y4)3•x5 

•x5
Simplify x6 and x5 by ADDING POWERS

(x2y4)3•x5 

x6y12
•x5 = x   y

                      Parentheses first:

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

(x-2y3)4•x10 

x   y
•x10
Simplify x-8 and x10 by ADDING POWERS

(x-2y3)4•x10 

x-8y12
•x10=
x   y
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