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Lecture 02 a algebraic expressions
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. Laws of Exponents
Whenever we have variables which contain
exponents and have equal bases, we can do
certain mathematical operations to them.
Those operations are called the “Laws of
Exponents”
bx
b = base x = exponent
11. Laws of Exponents
m n m n m m m
x x x xy x y
1. 2.
3. 4.
m
5 . ,
n
x
m
x
m
n
n n m
m m
m
m n mn
x
x x
b if n m then
x
x
a if m n then
x
y
y
x x
1
5 . ,
12. Other Properties of
Exponents
1 0 x
1 1
x
x
Any single number or variable is always to
the first power
1 1 1 1 1 3 3 a a 2x 2 x 2x
13. Basic Examples
x 2 x 3 x 23 x
5 3 x 4
x 43 x
12 3 xy 3 3 x y
14.
3
x
y
Basic Examples
3
3
x
y
7
4
x
x
x 7
4
x
3 1
5
7
x
x
1
x 75
2
1
x
15. More Examples
4 3 72aa 34 2 7 a 7 14a
2 3 2 5r 8r 2r 232 5 8 2 r 7 80r
3 3 xy 3 3 3 3 x y 3 3 27y x
2
a
2
3
b
2 2
a
2 2
2
3
b
2
2
4
9
b
a
2 5 3 2m n 13 23 53 2 m n 3 6 15 2 m n 6 15 8 n m
8 4
x
2
x
8 x 4
1
4x
3 2 1
3
5
9
3
z
z
9
1
3
z 53
2
1
3
z
3
z
2
16. More Examples
3 2 2 3x y z 7xyz 31 21 12 3 7 x y z 4 3 3 21x y z
2 3 8xy 3xy 2xy 111 213 8 3 2 x y 3 6 48y x
2 3 2 2 2 3x y 2xy 12 22 32 12 12 22 3 x y 2 x y
4 6 2 4 9x y 4x y 42 64 9 4 x y 6 10 36x y
3
2
3
5
ab
3
a b
1 3 3 3 1
3
a b
5
1 3 1 3 2 3
3
a b
3 9 3
5
a b
3 3 6
3
a b
9 3
a b
3 6
125
27
a b
9
3
a
6 3
125
27
b
6
a
3
125
27
b