matetica basica excercicios

Cursos da área de Tecnologia – Cálculo Diferencial e integral 1

OPERAÇÕES BÁSICAS E EXPRESSÕES

2

 1 1
−  ⋅ 
2 2
c) 
3
 1  2 
 −  
 2  



NUMÉRICAS

1) Calcule as potências a seguir:
a)

(−3) 2

b) − 3

d)

− (−2) 3

e)

g)

7

1

c)
f)

34

 1
− 
 3

3

− 23

i)

(−2)1

2
 
3

h)

2
j)  
3

2

Prof.: Luís Humberto Miquelino

3

6) Se n ∈ Z e a ∈ IR * , simplifique as expressões: 4

a 2( n +1) ⋅ a 3− n a 1− n a n+ 4 − a 3 ⋅ a n
d)
a4 ⋅ an

a) a 2 n+1 ⋅ a 1− n ⋅ a 3− n

0

c)

a 2 n + 3 ⋅ a n −1
b)
a 2( n −1)

l) 0 7

7) Simplifique as expressões:
2) Se n ∈ IN , calcule o valor de

a)

A = (−1) 2 n − (−1) 2 n+3 + (−1) 3n − (−1) n .

8 + 32 + 72 − 50
3

b) 128 − 3 250 + 3 54 − 3 16
c)
d)

3)Calcule:
a)

d)

g)

3 −1

b)

e)

(0,1) −2

1
 
3

h)

− (−3)

−1

( − 2) −1

1
2 −3

c)

−2

f)

a 3 ab 4 + b3 a 4 b + 3 a 4 b 4 − 3ab3 ab

− 3 −1

 3
− 
 2

8) Efetue as operações indicadas com as raízes:

−3

a)

3 ⋅ 12

b)

c)

(0,25)−3

i)

5 108 + 2 243 − 27 + 2 12

3
1
:
2
2

d)

4:4 2

f)

3

e)

3

3 ⋅3 2
3

4) Simplifique as expressões, supondo a⋅b ≠ 0.
a)

c)

(a

2

[(a

3

⋅ b3

) ⋅ (a

⋅ b2

2

3

⋅ b2

)

3

)]

2 3

b)

d)

9) Efetue as operações:
a) 2 3 3 5 − 2 20 − 45

(

(a ⋅ b )
(a ⋅ b )
4

2 3

2 2

 a 3 ⋅ b −4 
 −2 2 
 a ⋅b 



b)
3

c)
d)

e)

(a

3

) ⋅ (a ⋅ b )
(a ⋅ b )

⋅b

−2 −2
−1

−2 3

2 −3

f)

(a

−1

5) Calcule o valor das expressões:
a)

2 −1 − (−2) 2 + (−2) −1
2 2 + 2 −2

b)

3 2 − 3 −2
32 + 3−2

)

+ b −1 ⋅ (a + b )

−1

24 : 3 3

5 5 1
:
2
2

)

( 20 − 45 + 3 125 ): 2 5
(6 + 2 )⋅ (5 − 2 )
(2 3 + 3 2 )⋅ (5 3 − 2 2 )
(3 + 2 )
2

e)

10) Racionalize o denominador de cada