1. Laws of Exponents

2. Multiplication of Powersb
(a+b) x x = x • x9
x3•x4•x2 =
x =
x3y6
x2y4•xy2=
x2+1y4+2 =
3x3y•2xy2=
3•2 x3+1y1+2 =
6x4y3

3. Robert Duncan 2007 Alief Taylor Math Dept
Division of Powers a x
(a – b) = x x b
9x5 3x2 =
3x5-2 =
3x3
10x5y7z3 2x3y2z
5x2y5z2 =
5x5-3y7-2z3-1=
Robert Duncan 2007 Alief Taylor Math Dept

4. Robert Duncan 2007 Alief Taylor Math Dept
Powers of Powers b
(xa) =
xab
(x4)5 =
x4x5 =
x20
(x3y4)2 =
x3x2y4x2 =
x6y8
[(x4)2]3 =
x4x2x3 =
x24
Robert Duncan 2007 Alief Taylor Math Dept

5. Robert Duncan 2007 Alief Taylor Math Dept
Negative Exponents 1
x-a
x-a = 1 xa
and
= xa 1 x5
x-5 =
x2y-4 = x2 y4
Robert Duncan 2007 Alief Taylor Math Dept

6. Robert Duncan 2007 Alief Taylor Math Dept
Zero Exponent
x0 = 1
x4x-4 =
x4+(-4) =
x0 = 1
x3-3 =
x0 = 1 x3 =
Robert Duncan 2007 Alief Taylor Math Dept

7. x2y3 x4y8 1
x2y5
=x-2 y-5 =
x2-4 y3-8

8. 2x3y-3 2x-1y2
4x3+-1 y-3+2
=4x2y-1
4x2 y

9. 6x4yz3
3x2y3z4
2x4-2 y1-3z3-4
=2x2 y-2z-1
2x2
y2z

10. Negative Exponent Rule
4x3y4
5x2y8
5x2y-6
2y2
Product Rule •
Quotient Rule
(4•5)x3+2y4+-6
20x5y-2 = =
(5•2)x2y8+2
10x2y10
2x3
y12
2x5-2y-2-10
2x3y-12 = =
Negative Exponent Rule