# Laws of Exponents - TeacherWeb

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```					Laws of Exponents

x *x  x
4   8   12

( a * b)  a * b
3      3     3

3113
 315
318

By Chancy Nordick
Review
What exactly is a power function again?

A power function has two parts:

y
x
Review Continued
Where
x  x1 * x2 ........* xn 1 * xn
n

And

b     1
x         b
x
Multiplication Laws
What if we want to multiply two power functions?

2 4
Example:     x x

( xx)( xxxx)

xxxxxx
6
x
Multiplication Laws
In General

a b
x x x
a   b

Note: Bases must be the same!
a b
A few examples                  x x x
a   b

4 7
2 *2  2
4   7
2      11

3 x 4 x
3x
b *b      4x
b                      b   7x
First Law
 xm*xn = xm+n
 Notice that the bases have to be the same.
 Find    x2*x3
 Find    x3y*x4y7
 Find   z2x5y9*zx7y4
Multiplication Laws
Now, what about powers of powers?
Example:         2 3
(a )

2       2   2
a *a *a

(aa )(aa )(aa )
6
a
Multiplication Laws
In General

(x )  x
a b      ab
A few examples            (x )  x
a b      ab

2 2
6
3         3*6
2    18

x  x
28       2*8
x16
The Third law
 (xm)n = xmn
 Find   (x4)5
 Find   (x3y9)8
 Find   (2x3y4)3
Multiplication Laws
Finally, how do I deal with powers of a product?
3
Example     (h * j )

(h * j )(h * j )(h * j )

h*h*h* j * j * j

3      3
h *j
Multiplication Laws
In General

( xy )  x y
a        a   a
Second Law
 (xy)m = xmym
 The base does not have to be the same here.
 Find   (xy)7
 Find   (xy)5
 Find   (2x)3
Quick Review
a b
x x x
a   b

(x )  x
a b    ab

( xy )  x y
a   a      a
A few examples
(3* x )  9x 2
2

(ax)  (ax )  a x
23           6    6       6

(2t )3 ( t 2 )  8(t 3 )(t 2 )  8t 5

4 *2  2 * 2  2 *2  23 x
x            x   2x       x       2x   x
We’re done….

With the multiplication laws, before
We go on….
Stand up and Stretch!
Onward!

to the division laws
Division Laws
Example

7
x     xxxxxxx
3
          xxxx  x 4

x       xxx
Division Laws
In General

a
x      a b
b
 x ,x  0
x
a
A few Examples              x      a b
b
 x ,x  0
x
8
l           8 6
l 6
   l          l    2

x 4
3           ( x 4) 4
34
   3                3      x
The Fourth Law
 xm/xn =      xm-n
 The base has to be the same.
 Find     x5/x3
 Find    x3y2/x2y
Division Laws
Similar to Multiplication

3
h   h h h h3
 j  * *  3
    j j j  j
Division Laws
In General

a
x   x  a

 y  a ,y0
    y
a
x     xa
Examples              y   ya , y  0
 

3
4
3
4
        3
5      5

4     4
x       x
  
7       7 4
Quick Review of Division Laws
a
x      a b
b
 x ,x  0
x
a
x     x a

 y   ya , y  0
 
Laws of Exponents

Compute:        2 5

Laws of Exponents

Compute:        5 -2

Laws of Exponents

Compute:        0 2

Laws of Exponents

Compute:        2 0

Laws of Exponents

Compute:        0 0

Laws of Exponents

Compute: -          42

Laws of Exponents

Compute:        (-4) 2

Laws of Exponents

Compute: -          4-2

Laws of Exponents

Compute:        0.125 -2

Laws of Exponents

Compute:          (4 5 )(42)

Laws of Exponents

Compute:        (4 5 )2

10,485,676
Laws of Exponents

What is one-third of
399 ?