Question

Calcule o valor das expressões:

a) 4-¹ + $( \frac{x}{y} )$-¹ +2-²


b) (0,5)-² : 4-¹

2)Calcule

2.(-1)2919 + 3.(-1)3000 + 4 .(-1)4002 + 5.(-1)1001} 

Answer 1

Aplicando propriedades de potencias

a)
       $4^{-1} + (\frac{x}{y} ) ^{-1} + 2^{-2} \\ \\= \frac{1}{4} + \frac{y}{x} + \frac{1}{4} \\ \\ = \frac{2}{4} + \frac{y}{x} \\ \\ = \frac{1}{2} + \frac{y}{x}$

b)
       $(0,5)^{-2} : 4^{-1} \\ \\ = (\frac{1}{2}) ^{-2} : \frac{1}{4} \\ \\ = (\frac{2}{1})^2 x \frac{4}{1} \\ \\= 4x4 \\ \\ =16$

$2. (-1)^{2219} + 3.(-1)^{3000} +4. (-1)^{4002} +5. (-1)^{1001} \\ \\ =2.(-1)+3.(1)+4(1)+5.(-1) \\ \\ =-2+3+4-5 \\ \\ =0$