RST UVW

STO ELEMENTARNIH ZADATAKA
KOJE BI SVI TREBALI ZNATI RIJEŠITI
Koristeći ove formule trebali bi riješiti zadane zadatke:
100 Elementarnih zadataka
a
a
n
m
( abc)
POTENCIJE
a ⋅ a = a
n m n+
m
a : a = a
n m n−m
= a : a = a
m
n
( a )
m
n
(( a ) )
⎛a⎞
⎜
b
⎟
⎝ ⎠
1
−
n
n m n−m
n n n n
0
1
−1
1
n
n
z
1
n⋅
m
n⋅m⋅z
−n n n
m
n
−n
n
n
n
1 1
= =
1 n
a
n
a
m
n
n
a b c
a
a
a
b
⎛a⎞ ⎛b⎞
b
⎜
b
⎟ = ⎜ =
a
⎟
⎝ ⎠ ⎝ ⎠ a
a
a
−
a
a
a
a
a
a
=
=
=
=
=
=
a
1
=
a
1
=
n
a
=
=
a
a
m
=
1
=
1
n
a
a
m n m
n
1)
2)
3)
2 3
4) x : x
2 5
3 2 2
4 2
5) x : x : x
7 2 3
7 8 9
6) x ⋅ x : x =
7)
8)
9)
10)
8
3
3
2
( x ) =
4
5
3
(( x ) ) =
2 2
(( x ) ) ( x )
2 4
(( x ) ) ( x )
3
2
( ab ) =
11) :
12) 2
13)
⎛2
⎜ x y
⎝3
2
6 5
3
5 5
2 3
4
3
2 3⎞
2
⎛2
14) ⎜ ab ⎟ : 2
⎝3
⎠
15)
16)
x
⋅ x =
2 4 6
x ⋅x ⋅ x =
x ⋅x ⋅ x =
x
x
⎛
⎜
⎝
x
y
=
⎞
⎟
⎠
−1
=
=
=
−2 3
⋅ =
⎞
⎟
⎠
=
( ab )
⎛ x⎞ ⎛ y⎞
⎜ ⎟ ⋅ ⎜ ⎟ =
⎝ y⎠
⎝ x⎠
=
2
=
2
3 2 2
2
⎛a ⎞ ⎛ y ⎞ ⎛ y ⎞
17) ⎜ ⋅ : =
3 ⎟ ⎜ 3 ⎟ ⎜ 4 ⎟
⎝ y ⎠ ⎝a ⎠ ⎝a
⎠
18)
−1 −2 −3
⎛2⎞ ⎛1⎞ ⎛1⎞
⎜ ⎟ + ⎜ ⎟ − ⎜ ⎟ =
⎝3⎠ ⎝3⎠ ⎝2⎠
−1
0 0 0 1 ⎛1
⎞
19) 27 ⋅x
⋅y
⋅2
⋅ ⎜ ⎟ =
⎝3
⎠
1 −1
0 −1 ⎛1⎞ ⎛1⎞
−3
20) y ⋅2 ⋅⎜ ⎟ ⋅⎜ ⎟ ⋅ 2 =
⎝2⎠ ⎝5⎠
© M I M SRAGA 1999 / 2004
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