\(\frac{2^{18}.18^7.3^3+3^{15}.2^{15}}{2^{10}.6^{15}+3^{14}.15.4^{13}}\)= ?
thực hiện phép tính; a.\(\frac{2^{18}.18^7.3^3+3^{15}.2^{15}}{2^{10}.6^{15}+3^{14}.15.4^{13}}\)
Ta có:
\(A=\frac{2^{18}.18^7.3^3+3^{15}.2^{15}}{2^{10}.6^{15}+3^{14}.15.4^{13}}=\frac{2^{18}.\left(2.3^2\right)^7.3^3+3^{15}.2^{15}}{2^{10}.\left(2.3\right)^{15}+3^{14}.3.5.\left(2^2\right)^{13}}\)
\(=\frac{2^{18}.2^7.3^{14}.3^3+3^{15}.2^{15}}{2^{10}.2^{15}.3^{15}+3^{15}.5.2^{16}}=\frac{2^{25}.3^{17}+2^{15}.3^{15}}{2^{25}.3^{15}+3^{15}.2^{16}.5}=\frac{2^{15}.3^{15}.\left(3^2.2^{10}+1\right)}{2^{16}.3^{15}.\left(2^9+5\right)}\)
\(=\frac{3^2.2^{10}+1}{2^{10}+10}=\frac{9.1024+1}{1024+10}=\frac{9217}{1025}\)
Rút gọn:
a,\(\frac{15.\left(1352-41\right)}{\left(1352-41\right)\left(150-15\right)}\)
b,\(\frac{2^{10}.6^{15}+3^{14}.15.4^{13}}{2^{18}.18^7.3^3+3^{15}.2^{25}}\)
Tính :
\(\dfrac{2^{18}.18^7.3^3+3^{15}.2^{15}}{2^{10}.6^{15}+3^{14}.15.4^{13}}\)
mn giúp mình nha ko copy của người khác tự làm mình sẽ tick ở đây chỉ có công bằng !
\(=\dfrac{2^{18}\cdot3^{14}\cdot3^3\cdot2^7+3^{15}\cdot2^{15}}{2^{10}\cdot2^{15}\cdot3^{15}+3^{14}\cdot3\cdot5\cdot2^{26}}\)
\(=\dfrac{2^{25}\cdot3^{17}+3^{15}\cdot2^{15}}{2^{25}\cdot3^{15}+3^{15}\cdot5\cdot2^{26}}\)
\(=\dfrac{2^{15}\cdot3^{15}\left(2^{10}\cdot3^2+1\right)}{2^{25}\cdot3^{15}\left(1+5\cdot2\right)}=\dfrac{1}{1024}\cdot\dfrac{9217}{11}=\dfrac{9217}{11264}\)
tk
thực hiện phép tính; a.\(\frac{2^{18}.18^7.3^3+3^{15}.2^{15}}{2^{10}.6^{15}+3^{14}.15.4^{13}}\) - Hoc24
Rút gọn
a) \(\frac{2^{10}.6^{15}+3^{14}.15.4^{13}}{2^{18}.18^7.3^3+3^{15}.2^{25}}\) b) \(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}\)
thực hiện phép tính; \(\dfrac{2^{18}.18^7.3^3+3^{15}.2^{15}}{2^{10}.6^{15}+3^{14}.15.4^3}\)
\(=\dfrac{2^{18}\cdot3^3\cdot\left(3^2\cdot2\right)^7+3^{15}\cdot2^{15}}{2^{10}\cdot2^{15}\cdot3^{15}+3^{14}\cdot3\cdot5\cdot2^6}\)
\(=\dfrac{2^{25}\cdot3^{17}+3^{15}\cdot2^{15}}{2^{25}\cdot3^{15}+3^{15}\cdot5\cdot2^6}\)
\(=\dfrac{2^{15}\cdot3^{15}\left(2^{10}\cdot3^2+1\right)}{2^6\cdot3^{15}\left(2^{19}+5\cdot1\right)}=\dfrac{2^9\cdot9217}{524293}\)
Câu 1: Chứng tỏ rằng:
\(\frac{1}{20}+\frac{1}{21}+\frac{1}{22}+...+\frac{1}{26}+\frac{1}{27}>\frac{8}{27}\)
Câu 2: Tính:
\(D=\frac{2^{10}.6^{15}+3^{14}.15.4^{13}}{2^{18}.18^7.3^3+3^{15}.2^{25}}\)
#)Giải :
Câu 1 :
Đặt \(A=\frac{1}{20}+\frac{1}{21}+\frac{1}{22}+...+\frac{1}{27}\)
\(\Rightarrow A>\frac{1}{27}+\frac{1}{27}+...+\frac{1}{27}\)( 8 số hạng )
\(\Rightarrow A>\frac{8}{27}=\frac{8}{27}\)
\(\Rightarrow A>\frac{8}{27}\)
#~Will~be~Pens~#
Câu 1:(trội)
Ta có:\(\frac{1}{20}+\frac{1}{21}+...+\frac{1}{27}>\frac{1}{27}+\frac{1}{27}+...+\frac{1}{27}=\frac{8}{27}\left(đpcm\right)\)
Câu 2:\(D=\frac{2^{25}.3^{15}+3^{15}.5.2^{26}}{2^{25}.3^{17}+3^{15}.2^{25}}=\frac{2^{25}3^{15}\left(1+5.2\right)}{2^{25}3^{15}\left(3^2+1\right)}=\frac{11}{10}\)
Tính giá trị biểu thức sau:
1/ \(\frac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\).
2/ \(\frac{5.\left(2^2.3^2\right)^9.\left(2^2\right)^6-2.\left(2^2.3\right)^{14}.3^6}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)
3/ \(\frac{2^{12}.13+2^{12}.65}{2^{10}.104}+\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)
4/ \(\frac{5.4^{15}-9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)
5/ \(\frac{13.4^6.\left(28\frac{7}{13}-27\frac{5}{18}\right)}{59.2^{12}\left(\frac{5}{14}+\frac{5}{84}+\frac{5}{204}+\frac{5}{374}\right)}\)
Tặng người giải mỗi ngày ba điểm hđ :)
1/ \(\frac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\)
\(=\frac{5^{20}.3^{29}-3^{31}.5^{18}}{7.3^{29}.5^{18}-3^{29}.5^{19}}=\frac{3^{29}.5^{18}.\left(25-9\right)}{3^{29}.5^{18}.\left(7-5\right)}=\frac{16}{2}=8\)
CÁC BÀI CÒN LẠI TƯƠNG TỰ HẾT NHÉ E
Rút gọn B= 2^10×6^15+3^14×15×4^13/2^19×18^7×3-3^15×2^25. Mình cần gấp lắm,nhanh lên nhé.
B=2^10*(2*3)^15+3^14*3*5*(2^2)^13/2^19*(2*3^2)^7*3-3^15*2^25
B=2^10*2^15*3^15+3^15+3^15*5*2^26/2^19*2^7*3^14**3-3^15*2^25
B=2^25*3^15+5*2*3^15*2^25/2*2^25*3^15-3^15*2^25
B=1*2^25*3^15+10*2^25*3^15/2*2^25*3^15-2^25*3^15
B=2^25*3^15*(1+10)/2^25*3^15*(2-1)=11/1=11
B=2^10*6^15+3^14*15*4^13/2^19*18^7*3-3^15*2^25cái hàng cuối có dấu chấm đằng trước bỏ nhé cảm ơn
Tính nhanh :
A = 2 mũ 10 . 6 mũ 15 + 3 mũ 14 . 15 . 4 mũ 13 /
2 mũ 18 . 18 mũ 2 . 3 mũ 3 + 3 mũ 15 . 2 mũ 25
Giúp mk nha !!!