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CD
24 tháng 7 2016
A, B, C,... là tên của bài bạn nha
VD: A, 15+x=15
B, 16+14+14+14
12 tháng 2 2018
\(\frac{2^5.7+2^5}{2^5.5^2-2^5.3}=\frac{2^5.\left(7+1\right)}{2^5.\left(5^2-3\right)}=\frac{8}{25-3}=\frac{8}{22}=\frac{4}{11}\)
\(\frac{3^4.5-3^6}{3^4.13+3^4}=\frac{3^4.\left(5-3^2\right)}{3^4.\left(13+1\right)}=\frac{5-9}{14}=\frac{-4}{14}=\frac{-2}{7}\)
\(\frac{-2}{7}=\frac{-22}{77}\)
\(\frac{4}{11}=\frac{28}{77}\)
25 tháng 7 2016
A) \(\frac{8^{15}.3^{17}}{4^{23}.9^9}=\frac{2^{45}.3^{17}}{2^{46}.3^{18}}=\frac{2^{45}.3^{17}}{2^{45}.3^{17}.\left(2.3\right)}=\frac{1}{6}\)
B)\(\frac{28^{15}.3^{17}}{84^{16}}=\frac{\left(2^2.7\right)^{15}.3^{17}}{\left(2^2.3.7\right)^{16}}=\frac{2^{30}.7^{15}.3^{17}}{2^{32}.3^{16}.7^{16}}=\frac{2^{30}.7^{15}.3^{16}.3}{2^{30}.7^{15}.3^{16}.\left(2^2.7\right)}=\frac{3}{28}\)
C) \(\frac{3^{10}+6^2}{5.3^8+20}=\frac{3^{10}+2^2.3^2}{5.3^8+2^2.5}=\frac{3^2.\left(3^8+2^2\right)}{5.\left(3^8+2^2\right)}=\frac{9}{5}\)
D) \(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.3^6}{2^5.3^5.2^6}=\frac{2^7.3^6}{2^{11}.3^5}=\frac{2^7.3^5.3}{2^7.3^5.2^4}=\frac{3}{16}\)
F) \(\frac{5^4.20^4}{25^4.4^5}=\frac{5^4.\left(2^2.5\right)^4}{\left(5^2\right)^4.\left(2^2\right)^5}=\frac{5^4.2^8.5^4}{5^8.2^{10}}=\frac{5^8.2^8}{5^8.2^8.2^2}=\frac{1}{4}\)
G) \(\frac{5^5+25^2+5^2}{-151}=\frac{5^5+5^4+5^2}{-151}=\frac{5^2.\left(5^3+5^2+1\right)}{-151}=\frac{25.151}{-151}=-25\)
25 tháng 7 2016
A,\(\frac{8^{15}.3^{17}}{4^{23}.9^9}=\frac{\left(2^3\right)^{15}.3^{17}}{\left(2^2\right)^{23}.\left(3^2\right)^9}=\frac{2^{45}.3^{17}}{2^{46}.3^{18}}=\frac{1.1}{2.3}=\frac{1}{6}\)
B,\(\frac{28^{15}.3^{17}}{84^{16}}=\frac{28^{15}.3^{17}}{28^{16}.3^{16}}=\frac{1.3}{28.1}=\frac{3}{28}\)
C,\(\frac{3^{10}+6^2}{5.3^8+20}=\frac{3^{10}+3^2.2^2}{5.3^8+5.2^2}=\frac{3^2.\left(3^8+2^2\right)}{5.\left(3^8+2^2\right)}=\frac{3^2}{5}=\frac{9}{5}\)
D,\(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.\left(3^2\right)^3}{2^5.3^5.\left(2^3\right)^2}=\frac{2^7.3^6}{2^{11}.3^5}=\frac{3}{2^4}=\frac{3}{16}\)
F,\(\frac{5^4.20^4}{25^4.4^5}=\frac{5^4.5^4.4^4}{\left(5^2\right)^4.4^5}=\frac{5^8.4^9}{5^8.4^5}=\frac{1}{4}\)
G,xin lỗi mik ko lm đc câu này.
Nhưng mik cũng đã cố gắng làm giúp bn mấy câu trên. k cho mik nha.
RM
24 tháng 7 2017
\(A=2^0+2^1+2^2\)\(+2^3+...+\)\(2^{50}\)
\(2A=2+2^2+2^3+...+2^{51}\)
\(2A-A=A=2^{51}-2^0\)
\(B=5+5^2+5^3+...+5^{99}+5^{100}\)
\(5B=5^2+5^3+5^4+...+5^{100}+5^{101}\)
\(5B-B=4B=5^{101}-5\)
\(B=\frac{5^{101}-5}{4}\)
\(C=3-3^2+3^3-3^4+...+\)\(3^{2007}-3^{2008}+3^{2009}-3^{2010}\)
\(3C=3^2-3^3+3^4-3^5+...-3^{2008}+3^{2009}-3^{2010}+3^{2011}\)
\(3C+C=4C=3^{2011}+3\)
\(C=\frac{3^{2011}+3}{4}\)
\(S_{100}=5+5\times9+5\times9^2+5\times9^3+...+5\times9^{99}\)
\(S_{100}=5\times\left(1+9+9^2+9^3+...+9^{99}\right)\)
\(9S_{100}=5\times\left(9+9^2+9^3+...+9^{99}+9^{100}\right)\)
\(9S_{100}-S_{100}=8S_{100}=5\times\left(9^{100}-1\right)\)
\(S_{100}=\frac{5\times\left(9^{100}-1\right)}{8}\)
24 tháng 10 2023
A=20+21+22+23+...++23+...+250250
2�=2+22+23+...+2512A=2+22+23+...+251
2�−�=�=251−202A−A=A=251−20
�=5+52+53+...+599+5100B=5+52+53+...+599+5100
5�=52+53+54+...+5100+51015B=52+53+54+...+5100+5101
5�−�=4�=5101−55B−B=4B=5101−5
�=5101−54B=45101−5
�=3−32+33−34+...+C=3−32+33−34+...+32007−32008+32009−3201032007−32008+32009−32010
3�=32−33+34−35+...−32008+32009−32010+320113C=32−33+34−35+...−32008+32009−32010+32011
3�+�=4�=32011+33C+C=4C=32011+3
�=32011+34C=432011+3
�100=5+5×9+5×92+5×93+...+5×999S100=5+5×9+5×92+5×93+...+5×999
�100=5×(1+9+92+93+...+999)S100=5×(1+9+92+93+...+999)
9�100=5×(9+92+93+...+999+9100)9S100=5×(9+92+93+...+999+9100)
9�100−�100=8�100=5×(9100−1)9S100−S100=8S100=5×(9100−1)
�100=5×(9100−1)8S100=85×(9100−1)
23 tháng 9 2017
1,
a, \(11.11.11=11^3\)
b,\(55.5.5.13.13=55.5^2.13^2\)
c, \(3^7.3^{10}.3^2=3^{\left(7+10+2\right)}=3^{19}\)
d, \(2^5.2^6.2^7.2.2.2=2^5.2^6.2^7.2^3\)
e, \(2^9:2^3.2^4=2^6.2^4=2^{10}\)
2,
\(4^9:8^5=8\)
\(32^{10}:8^5=4^{10}.8^{10}:8^5=4^{10}.8^5\)
\(9^{15}:27^{10}=9^{15}:9^{10}.3^{10}=9^5.3^{10}\)( tự tính)
3,
Ta có:
\(7^{200}=7^{2.100}=\left(7^2\right)^{100}=49^{100}\)
\(2^{700}=2^{7.100}=\left(2^7\right)^{100}=128^{100}\)
Vì \(128^{100}>49^{100}\)nên \(2^{700}>7^{200}\)
5 tháng 3 2017
A/B=5.4^15.9^9-4.3^20.8^9/2^29.3618.6^19-7.2^29.27^6
=2^29.3618.(5.2-3^2)/2^28.3^18.(5.3-7.2)
=2.1/1
=2
vậy A:B=2
7 tháng 8 2016
Ta có:
\(8^3:8^4=\left(2^3\right)^3:\left(2^3\right)^4\)
\(=2^9:2^{12}=2^{9-12}=2^{-3}\)
Hình như có gì sai sai đó