ESERCIZI CON ESPONENTI LETTERALI e negativi

ESERCIZI CON ESPONENTI LETTERALI e negativi
1)
(a
2x +3y 2x +y
€
€
[a
x −y 2x −y
2 n +3
2)
2x −y x +y
) : (a )
(a )
⎧
⎪ ( a ) ⋅ ( a ) : a
⎨
3 n +3
3n +8
+
a n +3 ⋅ a n +6 : a 4
(an +2 )
n +3
⋅ a2
n +5 n
⎪⎩
(a ) ⋅ (a
n
⎧ 2n −1 −3 −n 2
⎫6
⎪ ( a ) : a ⋅ ( a 5 )
a n +4 ⎪
+ n +1 ⎬
3) ⎨
n n −1
a ⎪
⎪⎩
a
( )
⎭
2 3
)
⎫2
a ⎪
+ n +5 ⎬
a ⎪
⎭
[9a ]
4
€
[64a ]
18
€
[5a ]
n
€
6
5)
6)
€
7)
€
8)
€
€
4
⎧ x 2n +1 ⋅ x 3n −1 x n +1 ⋅ x n +2 ⎫
2 −3
⎨
⎬
+
−1
⋅
−x
[1]
( )
x 5n
x 2n −1
⎩
⎭
€
5
⎧ 2n −1 3n −1
⎫
: x )⋅ ( −x n +1 ) : ( −x 3 ) x 2n −1 ⋅ x 4 n −2 ⎪
⎪ ( x
−1
⎨
⎬ : ( x1−5n )
+
[2]
3−n
n −2
€
x
x
⎪
⎪
⎩
⎭
⎡
⎤ 3
n −3 n −2
n +3 −2
n +3 2
3n −10
⎢ 6+n n +4 ( x )
( x ) ⋅ ( x ) : x ⎥
€
⎢ x : x + 4 n n −5 +
⎥
[27x 6 ]
−2
−1
−n
n
−8
x (x )
⎢
⎥
(x ) : x
⎣
⎦
2
2 ⎛
⎧
⎫
5 n 2n ⎞
n 3n
3n n
n n 2
2n
⎨
⎬ : (12a n +1 ) e
A
=
−a
b
−5a
b
:
−a
b
:
−
a
b
+
3a
(
)(
)(
) ⎜⎝ 3 € ⎟⎠
Date le espressioni
⎩
⎭
[
€
€
€
]
]
[
]
⎡ 1 4 n −1 ⎛ 1 3n +1 ⎞ ⎤ −2 3n −4 2−n
B = 4⋅ ⎢ a
: ⎜ a ⎟ ⎥ ⋅ a
: a con
⎝ 4
⎠ ⎦
⎣ 2
€
uguali
(
3
2
9) 2a b : −5xy
(
€
[
]
[
)(
)
2
3
10) −4a b : −2ab
€
]
7+n
4)
€
3y 2 +10xy
[n = 1]
3 3 ⎛ 1 4 5 ⎞
xy : ⎜ − x y ⎟
⎝ 2
⎠
4
;
)
, stabilire per quale valore di n esse risultano
⎡ 2 3 −1 −2
⎢⎣− 5 a bx y ;
€
9x 2 y 3 z : ( −3x 3 y 2 z 4 )
;
[2ab
⎡⎛ a ⎞ −4 ⎤ 3 ⎡⎛ a ⎞ 2 ⎤ −5
⎛ 1 ⎞ −2 ⎡ ⎛ 1 2 ⎞ −1 ⎤
+ ⎜ a€⎟ + ⎢−⎜ − a ⎟ ⎥;
⎢⎜ − ⎟ ⎥ : €
⎢⎜ − ⎟ ⎥
⎝ 2 ⎠
⎣ ⎝ 3 ⎠ ⎦
⎣⎝ 2 ⎠ ⎦ ⎣⎝ 2 ⎠ ⎦
€ −2
€ −3
−3
−2
3
−3
−3
2
−1
2 −2
⋅ ( −x )
: ( x −2 ) ;
a
x
:
a
x
:
a
x
( ) ( ) ( )
−1
−2 −1
[(a ) ]
12) [( −x ) ] [
]
[
]
13) [( −3ab ) : ( −3ab )] : [ −2ab ( −ab ) c ] ⋅ ( 3ab c )
11)
2
4
3
2
2
3
3
2
2
2
−1 −1
−2
−2
⎤
3
− x −3 y −2 ⎥
⎦
2
;
[8a
−2
− 3x −1 yz −3 ]
; 4a −2 ]
[x
€
−12
; a16 x 2 ] ⎡ 3 −5 ⎤
⎢⎣− 4 a ⎥⎦ €
€