a)= 2021.2021-2020.(2021+1)
  = 2021.(2020+1)-2020.(2021+1)
  = (2021.2020)+2021-(2020.2021)-2020
  = 1

b) B= (1+2-3-4)+(5+6-7-8)+(9+10-11-12)...........+(2017+2018-2019-2020)+2021
    B= -4+(-4)+....................(-4)+2021
    B= -4x505+2021
    B= -2020 + 2021
    B = 1

a: \(A=21\cdot100-11\cdot100+90\cdot100+100\cdot125\cdot16\)

\(=100\left(21-11+90\right)+100\cdot2000\)

\(=100\left(10+90+2000\right)=2100\cdot100=210000\)

b: \(=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{28}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)

\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{28}\cdot3^{18}\left(5\cdot3-7\cdot2\right)}=2\)

\(=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{29}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{29}\cdot3^{18}\left(5\cdot3-7\right)}=\dfrac{10-9}{15-7}=\dfrac{1}{8}\)

\(\dfrac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)  (sửa \(-9^9\rightarrow.9^9\))

\(=\dfrac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)

\(=\dfrac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)

\(=\dfrac{2^{29}.3^{18}\left(15-9\right)}{2^{28}.3^{18}\left(15-14\right)}\)

\(=2.6=12\)

\(\dfrac{5.4^{15}.9^9+4.3^{20}.8^9}{5.2^{10}.6^{19}-7.2^{29}.27^6}=\dfrac{5.2^{30}.3^{18}+2^2.3^{20}.2^{27}}{5.2^{10}.2^{19}.3^{19}-7.2^{29}.3^{18}}\)

=\(\dfrac{5.2^{30}.3^{18}+2^{29}.3^{20}}{5.2^{29}.3^{19}-7.2^{29}.3^{18}}=\dfrac{2^{29}.3^{18}\left(5.2+3^2\right)}{2^{29}.3^{18}\left(5.3-7\right)}\)

=\(\dfrac{10+9}{15-7}=\dfrac{19}{8}\)

Bạn cho mình hỏi là 5.4 vs mấy cái tương tự là 5 nhân 4 hay 5,4 vậy?

Giải:

\(\dfrac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\) 

\(=\dfrac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\) 

\(=\dfrac{2^{29}.3^{18}.\left(5.2-3^2\right)}{2^{28}.3^{18}.\left(5.3-7.2\right)}\) 

\(=2\) 

Theo mk đề bài thế này mới đúng!

\(A=\dfrac{5.4^{15}.9^9-4.3^{20}.8^9}{7.2^{29}.27^6-5.2^9.6^{19}}\)

\(A=\dfrac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{7.2^{29}.3^{18}-5.2^9.2^{19}.3^{19}}\)

\(A=\dfrac{2^{29}.3^{18}.\left(5.2-3^2\right)}{2^{28}.3^{18}.\left(7.2-5.3\right)}\)

\(A=\dfrac{2.\left(10-9\right)}{14-15}=\dfrac{2}{-1}=-2\)

Chúc bạn học tốt!!!

\(A=\dfrac{5.4^{15}.9^9-4.3^{20}.8^9}{7.2^{29}.27^6-5.2^9.6^{19}}=\dfrac{5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^2\right)^9}{7.2^{29}.27^6-5.2^9.\left(2.3\right)^{19}}\)

\(=\dfrac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{7.2^{29}.3^{18}-5.2^9.2^{19}.3^{19}}\)

\(=\dfrac{2^{29}.3^{18}\left(5.2-3^2\right)}{2^{28}.3^{18}\left(7.2-5.3\right)}\)

\(=\dfrac{2\left(10-9\right)}{14-15}=\dfrac{2}{-1}=-2\)