Exponents and Polynomials
A. First Law of exponents
1. y 5 x10 ⋅ y 3 x 6
4. x 2 x 4
7. 3x 2 · 4 x 5
2. xy ⋅ x 2 y 3
5. b) y 3 y 6 y 2
8. 53 x 4 y · 52 xy 4
3. y ⋅ y ⋅ y 3 ⋅ y ⋅ y 2
6. x 5 y 2 · x 3 y 4
9. x 2 x 2 y 3 y 6 ⋅ x 4 x 6 y 2 y 2
10. 32 ⋅ 3⋅ 53
13.. 12 w 6 x 3 y ⋅ 12 3 w 7 x 2 y 3
11. 4 x 2 y 3 ⋅ 7 x 2 y 3
12. 11xy 2 ⋅ 11x 3 y
B. Second Law of Exponents:
( )
(
7. m 4 yx 3 w 4
(
10.. 5xy 2
(
6
1. ( x 7 ) 2
4. ( x 4 y 2 ) 3
)
2. y 4
5. (3x 2 y ) 3
)
( )
11. (3 x y ) (3 x y )
3
8. 3y 3
10
2 2
2
6
(
)
12. (2 wx ) (2
3
3
)
3. w y 2
6. (4 2 x 3 y 2 z ) 3
9. 5 6 x 3 y 3
3 2
3
5
2
C. Third Law of Exponents
y9
1. 4
y
y4
2. 9
y
w6
3. 6
w
x7
4. 3
x
y6
5. 10
y
x5 y7
6. 2 9
x y
w3v 4
7. 2 8
w v
20 w 3 y 6
8.
10 w 3 y 3
10 x 6 y
9.
5xy 4
10.
34 x 3 y 4
32 x 3 y 2
13.
1010 a 3 b 2 c 8
10 8 a 5 b 7 c 2
(x y )
(x y )
2
11.
3
(w
4 4
10
3 2
D. Simplify the following:
(4
1.
2
a 3b 4
) (4
2
5
a 3b 2
(4a b )
3
2 10
)
3
(4a bc ) (4 a b c )
2.
(4 a b c )
2
3 4
3
6
3
7
2
3 2
)
2
z4
( w8 y 3 ) 3
12.
5
2
w2 x 7
)
3
3.
7 2 x ⋅ 7 3x
6.
(x z )5
9.
3 1
7 4
(x )
12.
35 x − 5
34 x + 7
15..
(5x − 2x + 3)
18.
3x −8 y −5
2x −3 y −7
2
2 a ⋅ 2b
2c c
7. (3 )
7 x ⋅11x
2 x +1 3x −1
)
8. (2
4.
5
3
5.
4 2
7 5
4x
11. 2
10. (x y )
x
13..
x
−7x+3
⋅ 2 3x
2
+5x+4
4
5
14. x
2
7
2x −7
16. .
−3y −4
0
(12x y ) (3x
−3
28.
2
3
−5 2 −3
−1 4 −2
(4x y )
y )
−7
17. .
( 2x
)
−6 −4 −5
y