working with negative exponents when working with negative exponents, move the variable and change...
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Working with Negative Exponents
When working with negative exponents, move the variable and change the exponent
to positive.
When working with negative exponents, move the variable and change the exponent
to positive.
3
1
2x
31
2
x
3
2
x
When working with negative exponents, move the variable and change the exponent
to positive.
4
7
y
4
1
7y
When working with negative exponents, move the variable and change the exponent
to positive.
9
2
3
4
x
y
2
9
3
4
y
x
When working with negative exponents, move the variable and change the exponent
to positive.
7 5
3
2
5
x y
xz
3
7 5
2
5
z
xx y
3
8 5
2
5
z
x y
Simplifying Square Roots
21 122 423 924 1625 25
26 3627 4928 6429 81210 100
211 121212 144213 169214 196215 225
Simplify the Square Root
25 5
Simplify the Square Root
81 9
Simplify the Square Root
144 12
25 5
81 9
144 12
Perfect Squares
54 ?
72 ?
80 ?
Not Perfect Squares
Simplify the Square Root
1, 4, 9
16, 25, 36
49, 64, 81
100, 121, 144
169, 196, 225
What’s the biggest number here What’s the biggest number here that will go into 54 evenly?that will go into 54 evenly?
9 x 69 x 6
54
Simplify the Square Root
54 9 6 3 6 3 6
Simplify the Square Root
1, 4, 9
16, 25, 36
49, 64, 81
100, 121, 144
169, 196, 225
What’s the biggest number here What’s the biggest number here that will go into 72 evenly?that will go into 72 evenly?
36 x 236 x 2
72
Simplify the Square Root
72 36 2 6 2 6 2
Simplify the Square Root
1, 4, 9
16, 25, 36
49, 64, 81
100, 121, 144
169, 196, 225
What’s the biggest number here What’s the biggest number here that will go into 80 evenly?that will go into 80 evenly?
16 x 516 x 5
80
Simplify the Square Root
80 16 5 4 5 4 5
The square root of a negative number does not exist.
So, we say it is an imaginary number and we use the variable “i”.
The square root of a negative number does not exist.
So, we say it is an imaginary number and we use the variable “i”.
16 4i
The square root of a negative number does not exist.
So, we say it is an imaginary number and we use the variable “i”.
100 10i
Simplify the Square Root
1, 4, 9
16, 25, 36
49, 64, 81
100, 121, 144
169, 196, 225
What’s the biggest number here What’s the biggest number here that will go into 8 evenly?that will go into 8 evenly?
4 x 24 x 2
8 8i
Simplify the Square Root
8 8i4 2i 2 2i
2 2i
Multiplying Square Roots
Multiply the Square Roots
2 8 16 4
Multiply the Square Roots
5 20 100
10
Multiply the Square Roots
3 12 36
6
Fractions as exponents
3 54 Square Root
Cube Root
Fourth Root
Fifth Root
4 2
What do you multiply by itself to get 4?
3 27 3
What do you multiply by itself 3 times to get 27?
3 3 3 9 327
4 16 2
What do you multiply by itself 4 times to get 16?2 2 2 2 4 2 2
8 216
1
2as exponent
means 1
3as exponent
means3
1
4as exponent
means4
1
5as exponent
means5
1225 25 5
138 3 8 2
15x 5 x
1
2as exponent
means 1
3as exponent
means3
1
4as exponent
means4
1
5as exponent
means5
Numerator is 1
If the numerator is not 1, it becomes the exponent underneath the radical.
23x Outside Radical
Under Radical
If the numerator is not 1, it becomes the exponent underneath the radical.
23 x2
3x
If the numerator is not 1, it becomes the exponent underneath the radical.
79z 79 z
If the numerator is not 1, it becomes the exponent underneath the radical.
45y
45 y
If there are 2 exponents, multiply them.
3
1 42x
38x
If there are 2 exponents, multiply them.
2
4 35y
815y