CHỨNG MINH:
\(\frac{10^2+5.10^2+5^3}{6^3+3.6^2+3^3}=\frac{125}{27}\)
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B1: Tính
a) (1/4)44. (1/2)12
b) \(\frac{3^{17}.81^{11}}{27^{10}.9^{15}}
\)
c)\(\frac{14^{16}.21^{32}.35^{48}}{10^{16}.15^{32}.7^{96}}\)
d)\(\frac{\left(5^4-5^3\right)^3}{125^4}\)
e)\(\frac{10^3+5.10^2+5^3}{6^3+3.6^2+3^3}\)
tính
\(\frac{10^3+5.10^2+5^3}{6^3+3.6^2+3^3}\)
Rút gọn biểu thức:
1) \(\frac{10^3+5.10^2+5^3}{6^3+3.6^2+3^2}\)
2) \(\frac{5^3+5.5^2}{-8}\)
Giúp mik nhé!!!
1) Sửa đề :
\(\frac{10^3+5\cdot10^2+5^3}{6^3+3\cdot6^2+3^3}=\frac{10^3+5\cdot5^2\cdot2^2+5^3}{6^3+3\cdot2^2\cdot3^2+3^3}=\frac{5^3\cdot\left(2^3+2^2+1\right)}{3^3\cdot\left(2^3+2^2+1\right)}=\frac{5^3}{3^3}\)
2) Sửa đề :
\(\frac{5^3+3\cdot5^2}{-8}=\frac{5^2\cdot\left(5+3\right)}{-8}=\frac{-5^2\cdot8}{8}=-5^2=-25\)
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Thuc hien phep tinh;a/ frac{5}{15}+frac{14}{15}-frac{12}{9}+frac{2}{7}+frac{11}{25}b/ 4.frac{-1^3}{2}+frac{1}{2}c/ frac{10^3+5.10^2+5^3}{6^3+3.6^2+3^3}d/ frac{2^8.9^2}{6^4.8^2}e/(9frac{3}{4}:5,2+3,4.2frac{7}{34}):(-1frac{9}{16})f/frac{frac{2^3}{3}.frac{-3^2}{4}.left(-1right)^5}{frac{2^2}{5}.frac{-5^3}{6}}
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Thuc hien phep tinh;
a/ \(\frac{5}{15}+\frac{14}{15}-\frac{12}{9}+\frac{2}{7}+\frac{11}{25}\)
b/ \(4.\frac{-1^3}{2}+\frac{1}{2}\)
c/ \(\frac{10^3+5.10^2+5^3}{6^3+3.6^2+3^3}\)
d/ \(\frac{2^8.9^2}{6^4.8^2}\)
e/(\(9\frac{3}{4}:5,2+3,4.2\frac{7}{34}\)):(-1\(\frac{9}{16}\))
f/\(\frac{\frac{2^3}{3}.\frac{-3^2}{4}.\left(-1\right)^5}{\frac{2^2}{5}.\frac{-5^3}{6}}\)
\(\frac{15^5.10^5}{6^6.25^6}\)
2.\(\frac{\left(5^4.5^3\right)^3}{125^4}\)
\(\frac{15^5.10^5}{6^6.25^6}\)
\(=\frac{3^5.5^5.2^5.5^5}{3^6.2^6.5^{12}}\)
\(=\frac{3^5.2^5.5^{10}}{3^6.2^6.5^{12}}\)
\(=\frac{1}{3.2.5^2}\)
\(\frac{\left(5^4.5^3\right)^3}{125^4}\)
\(=\frac{\left(5^7\right)^3}{5^{12}}\)
\(=\frac{5^{21}}{5^{12}}\)
\(=5^9\)
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Bài 1 : Tính :a)frac{left(13frac{1}{4}-2frac{5}{27}-10frac{5}{6}right)times230frac{1}{5}+46frac{3}{4}}{left(1frac{3}{10}+frac{10}{3}right)divleft(12frac{1}{3}-14frac{2}{7}right)}b) frac{2^{12}times3^5-4^6times9^2}{left(2^4times3right)^6+8^4times3^5}-frac{5^{10}times7^3-25^5times49^2}{left(125times7right)^3+5^9times14^3}c)Pfrac{frac{1}{2}+frac{1}{3}+frac{1}{4}+....+frac{1}{2016}}{frac{2015}{1}+frac{2014}{2}+frac{2013}{3}+....+frac{1}{2015}}
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Bài 1 : Tính :
a)\(\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right)\times230\frac{1}{5}+46\frac{3}{4}}{\left(1\frac{3}{10}+\frac{10}{3}\right)\div\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)
b) \(\frac{2^{12}\times3^5-4^6\times9^2}{\left(2^4\times3\right)^6+8^4\times3^5}-\frac{5^{10}\times7^3-25^5\times49^2}{\left(125\times7\right)^3+5^9\times14^3}\)
c)P=\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{2016}}{\frac{2015}{1}+\frac{2014}{2}+\frac{2013}{3}+....+\frac{1}{2015}}\)
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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(2^2.3^2right)^9.left(2^2right)^6-2.left(2^2.3right)^{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(28frac{7}{13}-27frac{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 ...
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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
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Bài 3: Thực hiện phép tính
1) 2sqrt{5}-sqrt{125}-sqrt{80}+sqrt{605}
2) frac{10-2sqrt{10}}{sqrt{5}+sqrt{2}}+frac{8}{1-sqrt{5}}
3)sqrt{15-sqrt{216}}+sqrt{33-12sqrt{6}}
5)sqrt{frac{2-sqrt{3}}{2+sqrt{3}}}+sqrt{frac{2+sqrt{3}}{2-sqrt{3}}}
6)6sqrt{frac{16}{3}}-3sqrt{frac{1}{27}}-6sqrt{frac{4}{75}}
7)2sqrt{27}-6sqrt{frac{4}{3}}+frac{3}{5}sqrt{75}
8)frac{sqrt{3-sqrt{5}}.left(3+sqrt{5}right)}{sqrt{10}+sqrt{2}}
9)sqrt{2-sqrt{3}}left(sqrt{5}+sqrt{2}right)
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Bài 3: Thực hiện phép tính
1) \(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)
2) \(\frac{10-2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\frac{8}{1-\sqrt{5}}\)
3)\(\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{6}}\)
5)\(\sqrt{\frac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}\)
6)\(6\sqrt{\frac{16}{3}}-3\sqrt{\frac{1}{27}}-6\sqrt{\frac{4}{75}}\)
7)\(2\sqrt{27}-6\sqrt{\frac{4}{3}}+\frac{3}{5}\sqrt{75}\)
8)\(\frac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
9)\(\sqrt{2-\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)\)
Bài 1) Rút gọn biểu thức
a) \(\frac{2^7.9^3}{6^5.8^2}\)
b) \(\frac{6^3+3.6^2+3^3}{-13}\)
c) \(\frac{5^4.20^4}{25^5.4^5}\)
d)(\(\frac{5^4-5^3}{125^4}\) )
a.
\(\frac{2^7\times9^3}{6^5\times8^2}=\frac{2^7\times\left(3^2\right)^3}{\left(2\times3\right)^5\times\left(2^3\right)^2}=\frac{2^7\times3^6}{2^5\times3^5\times2^6}=\frac{3}{2^4}=\frac{3}{16}\)
b.
\(\frac{6^3+3\times6^2+3^3}{-13}=\frac{\left(2\times3\right)^3+3\times\left(3\times2\right)^2+3^3}{-13}=\frac{2^3\times3^3+3\times3^2\times2^2+3^3}{-13}=\frac{8\times3^3+3^3\times4+3^3}{-13}\)\(=\frac{3^3\times\left(8+4+1\right)}{-13}=\frac{27\times13}{-13}=-27\)
c.
\(\frac{5^4\times20^4}{25^5\times4^5}=\frac{\left(5\times20\right)^4}{\left(25\times4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}\)
d.
\(\left(\frac{5^4-5^3}{125^4}\right)=\frac{5^3\times\left(5-1\right)}{\left(5^3\right)^4}=\frac{5^3\times4}{5^{12}}=\frac{4}{5^9}\)
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a)\(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.\left(3^2\right)^3}{2^5.3^5.\left(2^3\right)^2}=\frac{2^7.3^6}{2^5.3^5.2^6}=\frac{3}{2^4}\)
b)\(\frac{6^3+3.6^2+3^3}{-13}=\frac{6.6^2+3.6^2+3^3}{-13}=\frac{6^2.\left(6+3\right)+3^3}{-13}=\frac{6^2.9+3^3}{-13}=\frac{6^2.3^2+3.3^2}{-13}=\frac{3^2.\left(6^2+3\right)}{-13}=\frac{3^2.39}{-13}=3^2.\left(-3\right)=-27\)
c)\(\frac{5^4.20^4}{25^5.4^5}=\frac{100^4}{100^5}=\frac{1}{100}\)
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làm nhanh giùm mình nha mình đang cần gấp
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