Transcript Multiplication & Division Rule for exponents
Multiplication and Division of Exponents Notes
x
Multiplication Rule
n x m
x n
m
In order to use this rule the base numbers being multiplied must be the same.
x
Example:
x
3
x
4 Written in multiplication form
x
x
x
x
x
x
x
7 Using Rule
x
3 4
x
7
Example 1 2 3 2 5 2*2*2 2 3 5 2 8 2*2*2*2*2
x
3 Example 2
x
5
x
4
x
3 5 4
x
12
x
Example 3
x
4
y
3
y
4
z
Remember
x
1 4
y
3 4
z x
x
1
x
5
y
7
z
Example 4 ( 2
x
3
y
5 )(3
xy
3 )(
x
2
y
) Multiply coefficients and add exponents of like bases 6
x
(3 1 2)
y
(5 3 1) 6
x
6
y
9
4 Example 5
x
5 ( 2
x
2
y
5
xy
2 ) In order to simplify you must distribute. Since you are multiplying when you distribute you must use the multiplication rule for exponents 8
x
5 2
y
20
x
5 1
y
2 8
x
7
y
20
x
6
y
2
2.
3, 4.
5.
6.
1.
You Try Simplify each expression
y
4
y
2 ( 3
x
2 )(5
x
)
y
6 15
x
3
x
3
x
4 (
a
3
b
2 )(
a
2
b
4 )
x
7
a
5
b
6 12
y
3 (4
y
2
y
) (
x
5
y
2
x
4
y
6 )
x
9
y
8
2.
3.
4.
1.
You Try Simplify (remember when adding only add coefficients of like terms) 3
x
3 (2
x
2 5
x
2) 2
x
(4
x
1) 4
x
(
x
5) (
x
2 6
x
8) 4
x
5 ( 2
x
3 6
x
) 12
x
6 6
x
5 15
x
4 6
x
3 8
x
2 2
x
4
x
2 20
x
x
2 6
x
8 5
x
2 26
x
8 8
x
8 24
x
6 12
x
6 8
x
8 36
x
6
Division Rule: If the bases are the same subtract the exponents
x m x n
x m
n x x
3 5
x
x x
x x
x
x x
x
2 OR
x
5
x
3
x
5 3
x
2 Always do top exponent minus bottom exponent
2.
3.
1.
x
2
y
6
xy
2 6
a
7
b
3
ab
2
x
5
x
3
x
Examples
x
2 1
y
6 2
xy
4 3
a
7 1
b
3 2 3
a
6
b
Divide coefficients, subtract exponents of the like bases.
x
5 8
x
3
x
13
x
3
x
13 3
x
10 Use multiplication rule on top, then use division rule
Special Cases ( zero power): any base raised to a power of zero equals 1
x
0 1 Here is why, when the number in the numerator is the same as the number in the denominator, the quotient is always 1.
2 4 2 4 2 * 2 * 2 * 2 2 * 2 * 2 * 2 1 So it makes sense that 2 4 2 4 2 4 4 2 0 1
1.
2.
3.
a
3
b
4
a
3
b
10
x
4
y
3
x
4
y
2
m
10 5
m
10
n
5 Examples Simplify
a
3 3
b
4 1
a
0
b
3 1
b
3
b
3 2
x
4 4
y
3 2 2
x
0
y
1 2 *1
y
2
y m
10 10
n
5 5
m
0
n
0 1*1 1