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NT
1
LH
1
7 tháng 9 2017
a) \(\dfrac{2^{15}.9^4}{6^6.8^3}=\dfrac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}=\dfrac{2^{15}.3^8}{3^6.2^6.2^9}=\dfrac{2^{15}.3^8}{3^6.2^{15}}=3^2=9\)
b) \(\dfrac{45^{15}.5^{15}}{75^{15}}=\dfrac{\left(9.5\right)^{15}.5^{15}}{\left(3.25\right)^{15}}=\dfrac{9^{15}.5^{15}.5^{15}}{3^{15}.25^{15}}=\dfrac{\left(3^2\right)^{15}.5^{30}}{3^{15}.\left(5^2\right)^{15}}\)
\(\dfrac{3^{30}.5^{30}}{3^{15}.5^{30}}=3^{15}=14348907\)
c) \(\dfrac{8^{10}+4^{10}}{8^4+4^{11}}=\dfrac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\dfrac{2^{30}+2^{20}}{2^{12}+2^{22}}=\dfrac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(1+2^{10}\right)}\)
\(=\dfrac{2^{20}}{2^{12}}=2^8=256\)
d) \(\dfrac{ \left(x^2\right)^5}{\left(x^5\right)^2}=\dfrac{x^{10}}{x^{10}}=1\)
TT
27 tháng 10 2017
a. \(-1\dfrac{5}{7}.15+\dfrac{2}{7}.\left(-15\right)+\left(-105\right).\left(\dfrac{2}{3}-\dfrac{4}{5}+\dfrac{1}{7}\right)\)
\(=\dfrac{-180}{7}+\dfrac{-30}{7}+\left(-105\right).\dfrac{1}{105}\)
\(=\dfrac{-180}{7}+\dfrac{-30}{7}+\left(-1\right)\)
\(=-31\)
b. \(\dfrac{2^{15}.9^4}{6^6.8^3}=\dfrac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}=\dfrac{2^{15}.3^8}{2^6.3^6.2^9}=\dfrac{2^{15}.3^6.3^2}{2^{15}.3^6}=3^2=9\)
DH
13 tháng 7 2017
a, \(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.2^8.5^4}{5^{10}.2^{10}}=\dfrac{1}{5^2.2^2}=\dfrac{1}{25.4}=\dfrac{1}{100}\)
b, \(\dfrac{2^7.9^3}{6^5.8^2}=\dfrac{2^7.3^6}{2^5.3^5.2^6}=\dfrac{3}{2^4}=\dfrac{3}{16}\)
c, \(\dfrac{45^{10}.5^{20}}{75^5}=\dfrac{5^{10}.3^{20}.5^{20}}{3^5.5^{10}}=5^{20}.3^{15}\)
d, \(\left(0,8\right)^5=\left(0,1\right)^5.8^5=\dfrac{1}{100000}.32768=0,32768\)
e, \(\dfrac{2^{15}.9^4}{6^6.8^3}=\dfrac{2^{15}.3^8}{2^6.3^6.2^9}=3^2=9\)
d, \(\dfrac{8^{20}+4^{20}}{4^{25}+64^5}=\dfrac{2^{60}+2^{40}}{2^{50}+2^{30}}=\dfrac{2^{40}.\left(2^{20}+1\right)}{2^{30}.\left(2^{20}+1\right)}=2^{10}=1024\)
Chúc bạn học tốt!!!
13 tháng 7 2017
\(\text{a) }\dfrac{5^4\cdot20^4}{25^5\cdot4^5}=\dfrac{5^4\cdot\left(5\cdot4\right)^4}{\left(5^2\right)^5\cdot4^5}=\dfrac{5^4\cdot5^4\cdot4^4}{5^{10}\cdot4^5}=\dfrac{5^8\cdot4^4}{5^{10}\cdot4^5}=\dfrac{1}{5^2\cdot4}=\dfrac{1}{25\cdot4}=\dfrac{1}{100}\)
\(\text{b) }\dfrac{2^7\cdot9^3}{6^5\cdot8^2}=\dfrac{2^7\cdot\left(3^2\right)^3}{\left(2\cdot3\right)^5\cdot\left(2^3\right)^2}=\dfrac{2^7\cdot3^6}{2^5\cdot3^5\cdot2^6}=\dfrac{2^7\cdot3^6}{2^5\cdot2^6\cdot3^5}=\dfrac{2^7\cdot3^6}{2^{11}\cdot3^5}=\dfrac{3}{2^4}=\dfrac{3}{16}\)
\(\text{c) }\dfrac{45^{10}\cdot5^{20}}{75^5}=\dfrac{\left(5\cdot9\right)^{10}\cdot5^{20}}{\left(25\cdot3\right)^5}=\dfrac{5^{10}\cdot9^{10}\cdot5^{20}}{25^5\cdot3^5}=\dfrac{5^{10}\cdot5^{20}\cdot\left(3^2\right)^{10}}{\left(5^2\right)^5\cdot3^5}=\dfrac{5^{30}\cdot3^{20}}{5^{10}\cdot3^5}=5^{20}\cdot3^{15}\)
\(\text{d) }\left(0.8\right)^5=\left(\dfrac{8}{10}\right)^5=\left(\dfrac{4}{5}\right)^5=\dfrac{4^5}{5^5}=\dfrac{64}{3125}\)
\(\text{e) }\dfrac{2^{15}\cdot9^4}{6^6\cdot8^3}=\dfrac{2^{15}\cdot\left(3^2\right)^4}{\left(2\cdot3\right)^6\cdot\left(2^3\right)^3}=\dfrac{2^{15}\cdot3^8}{2^6\cdot3^6\cdot2^9}=\dfrac{2^{15}\cdot3^8}{2^6\cdot2^9\cdot3^6}=\dfrac{2^{15}\cdot3^8}{2^{15}\cdot3^6}=3^2=9\)
\(f\text{) }\dfrac{8^{20}+4^{20}}{4^{25}+64^5}=\dfrac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}=\dfrac{2^{60}+2^{40}}{2^{50}+2^{30}}=\dfrac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}=2^{10}=1024\)
KV
18 tháng 9 2017
1.Tính
(0,25)4.1024=(1/4)4.1024=4
2.So sánh
291=(213)7=81927
535=(55)7=31257
Mà 8192>3125=> 81927>31257
=> 291>535
3. Tìm giá trị biểu thức
a) \(\dfrac{45^{10^{ }}.5^{20^{ }}}{75^{15}}=\dfrac{\left(3^{2^{ }}.5\right)^{10^{ }}.5^{20}}{^{ }\left(3.5^2\right)^{15}}=\dfrac{3^{20}.5^{30}}{3^{15}.5^{30}}=3^5=243\)
b)\(\dfrac{\left(0,8\right)^5}{\left(0,4\right)^6}=\dfrac{\left(2.0,4\right)^5}{0,4.0,4^5}=\dfrac{2^{5^{ }}.0,4^5}{0,4.0,4^5}=\dfrac{2^5}{0,4}=80\)
c)\(\dfrac{2^{15}.9^4}{6^6.8^3}=\dfrac{2^{15^{ }}.3^8}{3^6.2^6.2^9}=\dfrac{2^{15}.3^8}{3^6.2^{15}}=3^2=9\)
Tic hộ tui đi !!! chúc bn hok tôts 
2 tháng 8 2018
\(9^8:3^2=3^{16}:3^2=3^{14}\)
\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{\left(5.3^2\right)^{10}.5^{20}}{\left(5^2.3\right)^{15}}=\frac{5^{10}.3^{20}.5^{20}}{5^{30}.3^{15}}=3^5\)
\(\frac{2^{15}.9^4}{6^6.8^3}=\frac{2^{15}.3^8}{2^6.3^6.2^9}=\frac{2^{15}.3^8}{2^{15}.3^6}=3^2=9\)
2 tháng 8 2018
1) 98 : 32 =(32)8:32=32.8:32=316:32=316-2=314
2) (4510.520)/7515=[(5.23)10.520]/(53)15=(510.23.10.520)/53.15=(530.230)/545=230/515=(22)15/515=(4/5)15
3) (215.94)/(66.83)=[215.(32)4]/[(2.30)....
Bạn làm tương tự
hk tốt nha!!!
6 tháng 9 2018
\(\frac{2^{15}\cdot9^4}{6^6\cdot8^3}=\frac{2^{15}\cdot3^4\cdot3^4}{2^6\cdot3^6\cdot\left(2^4\right)^3}=\frac{2^{12}\cdot2^3\cdot3^8}{2^6\cdot3^6\cdot2^{12}}\)
\(=\frac{2^3\cdot3^2\cdot3^6}{2^3\cdot2^3\cdot3^6}=\frac{3^3}{2^3}\)
\(=\frac{27}{8}\)
6 tháng 9 2018
\(\frac{2^{15}.9^4}{6^6.8^3}=\frac{\left(2^3\right)^5.\left(3^2\right)^4}{6^6.8^3}=\frac{8^5.3^8}{6^6.8^3}\)
\(=\frac{8^2.3^8}{6^6}=\frac{64.6561}{46656}=\frac{64.6561}{64.729}\)
\(=\frac{6561}{729}=9\)
NK
1
23 tháng 10 2020
\(\frac{2^{15}.9^4}{6^6.8^3}=\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}=\frac{2^{15}.3^8}{2^6.3^6.2^9}=2.3^2=2.9=18\)
\(\dfrac{2^{15}.9^4}{6^6.8^3}=\dfrac{2^{15}.3^8}{2^6.3^6.2^9}=3^2=9\)
\(\dfrac{2^{15}.9^4}{6^6.8^3}=\dfrac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}=\dfrac{2^{15}.3^8}{2^6.3^6.2^9}=\dfrac{3^8}{3^6}=3^2=9\)