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 ⎥⎦ € €