1.
[tex]a) \ (2x)^{5} = 2^{5}\cdot x^{5} = 32x^{5}\\\\b) \ (-4x^{2})^{2} = (-4)^{2}\cdot(x^{2})^{2} = 16\cdot x^{2\cdot2} =16x^{4}\\\\c) \ (-x^{3}y^{2})^{3} = (-x^{3})^{3}\cdot(y^{2})^{3} =(-x)^{3\cdot3}\cdot y^{2\cdot3} =-x^{9}y^{6}\\\\d) \ (\frac{-5x^{2}}{3y})^{3} = \frac{(-5)^{3}\cdot x^{2\cdot3}}{3^{3}\cdot y^{3}}=-\frac{125x^{6}}{27y^{3}}[/tex]
2.
miliard = 1 000 000 000 = 10⁹
bilion = 1 000 000 000 000 = 10¹²
milion = 1 000 000 = 10⁶
[tex]\frac{100\cdot10^{9}}{100} = 10^{9} \ razy\\\\\frac{100\cdot10^{12}}{10\cdot10^{6}} = \frac{10^{2}\cdot10^{12}}{10^{1+6}} =\frac{10^{2+12}}{10^{7}} = \frac{10^{14}}{10^{7}} = 10^{14-7} = 10^{7} \ razy[/tex]
Odp. 100 miliardów jest 10⁹ razy większe od stu.
100 bilionów jest 10⁷ razy większe od 10 milionów.
