multiplication and division of exponents notes by: tamiya, chris, shelby, qua von
TRANSCRIPT
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