Question

1.Przedstaw każdą z podanych liczb w postaci:
-potęgi o podstawie 2 lub 3
1
-potęgi o wykładniku 3 lub 4
0

2.Oblicz:
a) ½ × [(-1)⁸ + (-1)⁸]
b) (-3⅓)³ × 0,3⁴ - (-½)³ × (⅓)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) ÷ (-0,3)²

Answer 1

2.Oblicz:
a) ½ × [(-1)⁸ + (-1)⁸]=½×(-2)⁸=½×256 = 128

b) (-3⅓)³ × 0,3⁴ - (-½)³ × (⅓)²=(-10/3)³×(3/10)⁴-(-⅛)×1/9 = (-1000/27)×(81/10000)+1/72 = -81000/270000+1/72= - 3/10+1/72 = -108/360+5/360=-103/360

c) (1⅓)³ × (-3¾)² ÷ 3 - (⅓)² = 64/27×(-225/16):3+1/9 = 100/3:3+1/9 = 100/9+1/9 = 101/9

d) (-0,3)² ÷ 0,1 - 0,2³ × (2½)² = 0,09:0,1-0,008×25/4 = 0,9-0,05=0,85

e) (-0,1)⁴ × 20³ + (1½) ÷ (-0,3)²=0,0001×8000+(3/2):(9/100)=8/10+50/3 = 24/30+500/50=524/30 = 17 i 14/40=17,35