Multiplication and Division

of Exponents Notes

By: Tamiya, Chris , Shelby , Qua von

Multiplication Rule

Xn.Xm=Xn+m

In order to use this rule the base numbers being multiplied must be the same

Example: X4.X4

Written in multiplication form X.X.X.X.X.X.X

Using form X3+4=X7

Example 1

23.25

2*2*2 2*2*2*2*2

23+5

28

Example 2

x3.x5.x4

x3+5+4

x12

Example 3

x.x4.y4.z

Remember x=x1

x1+4y4z

x5y4z

Example 4

(-2x3y5)(3xy3)(x2y)

Multiply coefficients and add exponents of like bases

-6x(3+1+2)y(5+3+1)

-6x6y9

Example 5

4x5(-2x2y+5xy2)In order to simplify you must distribute . Since you are multiplying when you distribute

you must use the multiplication rule for exponents.

4x5 * -2x2y + 4x5 * 5xy2

-8x5+2y + 20x5+1y2

-8x7+20x6y2

Dividing Exponents

+You can divide exponential expressions, leaving the answers as exponential expressions, as long as the bases are the same. To divide exponents (or powers) with the same base, subtract the exponents. Division is the opposite of multiplication, so it makes sense that because you add exponents when multiplying numbers with the same base, you subtract the exponents when dividing numbers with the same base.

Dividing Exponents Example

210/24=210-4=26

Any number to the power of zero equals 1, as long as the base number is not 0

Try It Yourself!

1. 15.19=

2. 73.72=

3. 26/23=

4. 49/49=

5. 5.53/52=

The Answers

1. 15.19=114

2. 73.72=75

3. 26/23=23

4. 49/49=40= 40-0=1

5. 5.53/52=52

Almost Finish

We need to address Powers Property

Power of a Power Property

To find a power of a power, multiply the exponents.

(52)4 = 5 2 •4 = 58

Power of a Power Property

You Try!!

(y2)4

[(-33)]2

[(a+1)2]5

Power of a Power Property

You Try!!

(y2)4 = y2•4 = y8

[(-33)]2 = (-3)3•2 = (-3)6

[(a+1)2]5 = (a+1)2•5 = (a+1)10

Power of a Product Property

To find a power of a product, find the power of each factor and multiply.

(2 • 3)6 = 26 • 36 = 64 x 729 = 46,656

-(2w)2 = -(2 • w)2 = -(22 • w2) = -4w2

Power of a Product Property

You Try

(6 • 5)2 =

Power of a Product Property

You Try

(6 • 5)2 = 62 • 52

= 36 • 25

= 900

Power of a Product Property

You Try

(4yz)3 =

Power of a Product Property

You Try

(4yz)3 = ( 4 • y • z)3

= 43 • y3 • z3

= 64y3z3

Using All Properties (expect division)

You Try

(4x2y)3 • x5

Using All Properties (expect division)

You Try

(4x2y)3 • x5

= 43 • (x2)3 • y3 • x5

= 64 • x6 • y3 • x5

= 64x11y3

THE END