\(^{\dfrac{2^{10}.3^8+5.4^5.3^8}{2^{10}.27^3-2^{10}.9^4}}\) Rút Gọn
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Những câu hỏi liên quan
H9
HT.Phong (9A5)
CTVHS
29 tháng 10 2023
a) \(\dfrac{2}{5}-\dfrac{3}{15}\)
\(=\dfrac{2}{5}-\dfrac{3:3}{15:3}\)
\(=\dfrac{2}{5}-\dfrac{1}{5}\)
\(=\dfrac{1}{5}\)
b) \(\dfrac{9}{27}-\dfrac{2}{9}\)
\(=\dfrac{9:3}{27:3}-\dfrac{2}{9}\)
\(=\dfrac{3}{9}-\dfrac{2}{9}\)
\(=\dfrac{1}{9}\)
c) \(\dfrac{18}{24}-\dfrac{4}{8}\)
\(=\dfrac{18:6}{24:6}-\dfrac{4:2}{8:2}\)
\(=\dfrac{3}{4}-\dfrac{2}{4}\)
\(=\dfrac{1}{4}\)
d) \(\dfrac{6}{16}-\dfrac{10}{64}\)
\(=\dfrac{6\times2}{16\times2}-\dfrac{10:2}{64:2}\)
\(=\dfrac{12}{32}-\dfrac{5}{32}\)
\(=\dfrac{7}{32}\)
12 tháng 6 2017
\(1,\)
\(\dfrac{45^2.3^8.10^5}{5^5.3^7.18^5}\)
\(=\dfrac{3^4.5^2.3^8.2^5.5^5}{5^5.3^7.2^5.3^{10}}\)
\(=\dfrac{3^{12}.2^5.5^7}{5^5.3^{17}.2^5}\)
\(=\dfrac{1.5^2}{3^5.1}\)
\(=\dfrac{25}{243}\)
\(2,\)
\(\dfrac{4^5.9^4+2.6^9}{2^{10}.3^8+6^8.20}\)
\(=\dfrac{2^{10}.3^8+2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}\)
\(=\dfrac{2^{10}.3^8+2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}\)
\(=\dfrac{2^{10}.3^8.4}{2^{10}.3^8.6}\)
\(=\dfrac{2^{12}.3^8}{2^{11}.3^9}\)
\(=\dfrac{2}{3}\)
\(3,\)
\(\dfrac{15.3^{11}+4.27^4}{9^7}\)
\(=\dfrac{3.5.3^{11}+2^2.3^{12}}{3^{14}}\)
\(=\dfrac{5.3^{12}+2^2.3^{12}}{3^{14}}\)
\(=\dfrac{3^{12}\left(5+2^2\right)}{3^{14}}\)
\(=\dfrac{3^{12}.9}{3^{14}}\)
\(=\dfrac{3^{14}}{3^{14}}\)
\(=1\)
\(4,\)
\(\dfrac{4^7.2^8}{3.2^{15}.16^2-5^2\left(2^{10}\right)^2}\)
\(=\dfrac{2^{22}}{3.2^{23}-5^2.2^{20}}\)
\(=\dfrac{2^{22}}{2^{20}.\left(-1\right)}\)
\(=\dfrac{2^{22}}{-2^{20}}\)
\(=-4\)
* Mấy bài còn lại tương tự đấy bạn tự làm đi
Mình mỏi tay lắm rồi
12 tháng 6 2017
P/s:khuyến khích tự làm,chỉ làm mẫu 1 câu:
1)\(\dfrac{45^2.3^8.10^5}{5^5.3^7.18^5}=\dfrac{\left(5.9\right)^2.3.3^7.\left(2.5\right)^5}{5^5.3^7.\left(2.9\right)^5}\)\(=\dfrac{5^2.9^2.3.3^7.2^5.5^5}{5^5.3^7.2^5.9^5}\)\(=\dfrac{5^2.9^2.3.1.1.1}{1.1.1.9^5}\)\(=\dfrac{5^2.9^2.3}{9^5}=\dfrac{5^2.9^2.3}{9^2.9^3}=\dfrac{5^2.3}{9^3}=\dfrac{75}{729}=\dfrac{25}{243}\)
31 tháng 12 2022
a)= 2021.2021-2020.(2021+1)
= 2021.(2020+1)-2020.(2021+1)
= (2021.2020)+2021-(2020.2021)-2020
= 1
31 tháng 12 2022
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
8 tháng 7 2021
Ta có: \(C=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{4}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\dfrac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)\left(1+\sqrt{2}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=1+\sqrt{2}\)
8 tháng 7 2021
Ta có: \(B=\dfrac{\sqrt{2-\sqrt{3}}+\sqrt{4-\sqrt{15}}+\sqrt{10}}{\sqrt{23-3\sqrt{5}}}\)
\(=\dfrac{\sqrt{4-2\sqrt{3}}+\sqrt{8-2\sqrt{15}}+2\sqrt{5}}{3\sqrt{5}-1}\)
\(=\dfrac{\sqrt{3}-1+\sqrt{5}-\sqrt{3}+2\sqrt{5}}{3\sqrt{5}-1}\)
=1
28 tháng 10 2023
a: \(\dfrac{15}{8}-\dfrac{13}{8}=\dfrac{15-13}{8}=\dfrac{2}{8}=\dfrac{1}{4}\)
b: \(\dfrac{7}{15}-\dfrac{2}{15}=\dfrac{7-2}{15}=\dfrac{5}{15}=\dfrac{1}{3}\)
c: \(\dfrac{11}{12}-\dfrac{2}{12}=\dfrac{11-2}{12}=\dfrac{9}{12}=\dfrac{3}{4}\)
d: \(\dfrac{19}{7}-\dfrac{5}{7}=\dfrac{19-5}{7}=\dfrac{14}{7}=2\)
29 tháng 10 2023
a: \(\dfrac{3}{9}\times\dfrac{5}{4}=\dfrac{5}{4}\times\dfrac{1}{3}=\dfrac{5\times1}{4\times3}=\dfrac{5}{12}\)
b: \(\dfrac{10}{15}\times\dfrac{3}{5}=\dfrac{3}{5}\times\dfrac{2}{3}=\dfrac{3\times2}{5\times3}=\dfrac{2}{5}\)
c: \(\dfrac{5}{8}\times\dfrac{4}{12}=\dfrac{5}{8}\times\dfrac{1}{3}=\dfrac{5}{3\times8}=\dfrac{5}{24}\)
d: \(\dfrac{9}{27}\times\dfrac{3}{21}=\dfrac{1}{7}\times\dfrac{1}{3}=\dfrac{1\times1}{7\times3}=\dfrac{1}{21}\)
19 tháng 7 2021
a) Ta có: \(P=\left(\dfrac{x+3}{x-9}+\dfrac{1}{\sqrt{x}+3}\right):\dfrac{\sqrt{x}}{\sqrt{x}-3}\)
\(=\dfrac{x+3+\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\cdot\dfrac{\sqrt{x}-3}{\sqrt{x}}\)
\(=\dfrac{x+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+3\right)}\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}+3}\)
b) Ta có: \(x=\sqrt{27+10\sqrt{2}}-\sqrt{18+8\sqrt{2}}\)
\(=5+\sqrt{2}-4-\sqrt{2}\)
=1
Thay x=1 vào P, ta được:
\(P=\dfrac{1+1}{1+3}=\dfrac{2}{4}=\dfrac{1}{2}\)
18 tháng 2 2023
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: \(=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{28}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{28}\cdot3^{18}\left(5\cdot3-7\cdot2\right)}=2\)
Lời giải:
Gọi biểu thức là $A$
\(A=\frac{2^{10}.3^8+5.(2^2)^5.3^8}{2^{10}.(3^3)^3-2^{10}.(3^2)^4}=\frac{2^{10}.3^8+5.2^{10}.3^8}{2^{10}.3^9-2^{10}.3^{8}}\)
\(=\frac{2^{10}.3^8(1+5)}{2^{10}.3^8(3-1)}=\frac{6}{2}=3\)