Question

Thực hiện các phép tính sau:

a, (-14) . (-125) . (+3) . (-8)

b, (-25) . 68+(-34) . (-250)

c, D= 2¹⁰⁰ - 2⁹⁹ -2⁹⁸ - ... - 2² - 2 -1.

M.n giúp mk với

Answer 1

\(a,\left(-14\right)\cdot\left(-125\right)\cdot\left(+3\right)\cdot\left(-8\right)\\ =\left[\left(-125\right)\cdot\left(-8\right)\right]\cdot\left[3\cdot\left(-14\right)\right]\\ =1000\cdot\left(-42\right)\\ =-42000\)

Xem lại đề câu b nhé

\(D=2^{100}-2^{99}-2^{98}-...-2^2-2-1\\ =2^{100}-\left(2^{99}+2^{98}+...+2^2+2+1\right)\\ \text{Đặt }G=2^{99}+2^{98}+...+2^2+2+1\\ 2G=2^{100}+2^{99}+...+2^3+2^2+2\\ 2G-G=\left(2^{100}+2^{99}+...+2^3+2^2+2\right)-\left(2^{99}+2^{98}+...+2^2+2+1\right)\\ G=2^{100}-1\\ D=2^{100}-G\\ =2^{100}-\left(2^{100}-1\right)\\ =2^{100}-2^{100}+1\\ =1\)

Answer 2

b/(-25).34.2+/(-34).(-250)/

=(-50).34+34.250

=34.(-50+250)

=34.200

=6800

Answer 3

c/2D=2.(2¹⁰⁰-2⁹⁹-...-2²-2-1)

=2¹⁰¹-2¹⁰⁰-...-2³-2²-2

2D-D=2¹⁰¹-2¹⁰⁰-...-2³-2²-2-(2¹⁰⁰-2⁹⁹-2²-2-1)

D=2¹⁰¹-2.2¹⁰⁰⁺¹

D=2¹⁰¹-2¹⁰¹+1=1

Answer 4

a) -42000

b) 6800