Question

Daję naj ;D czyli 20 pkt ^^ oto zadanie ;p proszę o jak najszybszą odpowiedź ;]

1.

a) ½ × [(-1)⁸ + (-1)⁸] =

b) (-3⅓)³ × 0,3 ⁴ -(- ½)³ × (1⅓)² =

c) (1⅓)³ ×(- 3¾)² : 3 - (⅓)² =

d)(-0,3)² : 0,1 - 0,2³ × (2½)²=

e) (-0,1)⁴ × 20³ + (1½)³ : (-0,3)² =

2. a) 81×(-3)⁵ × (-27)=

b) (-1/32) ×1/16 ×(½)⁶=

c) 36×(-6)⁷ ×(-6)⁸

_______________

6( do potęgi 14) : (-6)

(-1/32) - to jest ułamek =)

1/16 - to jest ułamek =)

3. zapisz liczbę 100₂ w systemie dzieiskatkowym ;]

Answer 1

1.

a) ½ × [(-1)⁸ + (-1)⁸] =

½×[(-1)⁸+(-1)⁸]=

= 1/2*[ 1 +1] =

= (1/2)*2=

= 1

b) (-3⅓)³ × 0,3 ⁴ -(- ½)³ × (1⅓)² =

(-3⅓)³×0,3⁴-(-½)³×(1⅓)²=

=(-10/3)³×(3/10)⁴- (-1/8)*(16/9)=

= (-1000/27)*(81/10000) - (-2/9) =

=  3/10 +2/9 =

= 27/90 + 20/90 =

= 47/90

 

c) (1⅓)³ ×(- 3¾)² : 3 - (⅓)² =

  (4/3)³ *(- 15/4)² :3 - (1/3)²=

= 64/27 * 225/16 * 1/3 - 1/9 =

= 100/9 - 1/9 = 99/9 = 11

 

d)(-0,3)² : 0,1 - 0,2³ × (2½)²=

 

(-3/10)² :(1/10) - (2/10)³*(5/2)² =

= (9/1000*(10/1) - (8/1000)*(25/4) =

= 9/10 -1/20 =

= 18/20 -1/20 =

= 17/20 =

= 85/100= 0,85

 

e) (-0,1)⁴ × 20³ + (1½)³ : (-0,3)² =

 

(-1/10)⁴*20³ + (3/2)³ : (-3/10)²=

= (1/10000)*8000 + (27/8) : (9/100) =

= 8/10 + (27/8)*(100/9) =

= 8/10 + 75/2 =

= 8/10 + 375/10 =

= 383/10 =

= 38,3

 

2. a) 81×(-3)⁵ × (-27)=

= 3⁴*(-3)⁵ * (-3)³=

= 3⁴* (-3)^(8)=

= 3⁴* 3^(8) =

= 3^12    ( ozn. 3 do potęgi 12)

 

b) (-1/32) ×1/16 ×(½)⁶=

=(-1/2)^(5) * (1/2)⁴*(1/2)^(6)=

= (-1/2)^(5)*  (1/2)^(10)=

= -(1/2)^(5) *(1/2)^(10) =

= - (1/2)^(15)

 

c) 36×(-6)⁷ ×(-6)⁸

_______________

6( do potęgi 14) : (-6)

 

Obliczam licznik  L =  36 *(-6)⁷ *(-6)⁸

                         L = 6² * (-6)^(15)

                         L =(- 6)² * (-6)^(15)

                         L = (- 6)^(17)

Obliczam mianownik  M = 6 ^(14) : (-6)

                                M = (-6)^(14)  : (-6)

                                M = (-6)^(13)

 

Obliczam cały ułamek L :M = (-6)^(17) : (-6)^13

                                 L :M = (-6)^(17-13)

                                 L :M = (-6)^(4) = (-6)*(-6)*(-6)*(-6) = 6⁴

                                 L:M = 6⁴= 1296

 

(-6)^(4)  - ozna. (-6) do potegi 4

(-6)^4 = 6^4  ( bo jest to potęga parzysta) 

                   

Answer 2

1.

½ × [(-1)⁸ + (-1)⁸] =½x(1+1)=½x2=1

 

 

2.

81×(-3)⁵ × (-27)=3⁴x(-3)⁵x(-3)³=3⁴x3⁸-3¹²

(-1/32) ×1/16 ×(½)⁶=(-½)⁵x(½)⁴x(½)⁶=(-½)¹⁵

c) 36×(-6)⁷ ×(-6)⁸=6²x(-6)⁷x6⁸=(-6)¹⁷  = (-6)¹⁷ : (-6)¹³ = (6)⁴

6¹⁴:(-6)             -6¹⁴:6       (-6)¹³

 

3.100=10²