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4 tháng 1 2022
\(\dfrac{45^{10}\cdot5^{20}}{75^{15}}=\dfrac{\left(3^2\cdot5\right)^{10}\cdot5^{20}}{\left(3\cdot5^2\right)^{15}}=\dfrac{3^{20}\cdot5^{10}\cdot5^{20}}{3^{15}\cdot5^{30}}=3^5=243\\ \dfrac{6^6+6^3+3^3+3^6}{-73}=\dfrac{46656+216+27+729}{-73}=-\dfrac{47628}{73}\\ \dfrac{27^7+3^{15}}{9^9-27}=\dfrac{\left(3^3\right)^7+3^{15}}{\left(3^2\right)^9-3^3}=\dfrac{3^{21}+3^{15}}{3^{18}-3^3}=\dfrac{3^{15}\left(3^6+1\right)}{3^3\left(3^{15}-1\right)}=\dfrac{3^5\cdot730}{3^{15}-1}\\ \dfrac{8^{20}+4^{20}}{4^{25}+64^5}=\dfrac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}=\dfrac{2^{60}+2^{40}}{2^{50}+2^{30}}=\dfrac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}=2^{10}=1024\)
2 tháng 5 2017
\(\dfrac{\text{45^{10^{ }}}.5^{10}}{75^{10}}=\dfrac{9^{10}.5^{10}.5^{10}}{5^{10}.5^{10}.3^{10}}=\dfrac{9^{10}}{3^{10}}=3^{10}\)
2 tháng 5 2017
\(\dfrac{\left(0,8\right)^5}{\left(0,4\right)^6}=\dfrac{2^5.\left(0,4\right)^5}{\left(0,4\right)^6}=\dfrac{2^5}{0,4}=\dfrac{32}{0,4}=80\)
10 tháng 12 2017
M=\(\dfrac{8^{20}+4^{20}}{4^{25}+64^5}=\dfrac{4^{20}\left(2^{20}+1\right)}{4^{25}+4^{15}}=\dfrac{4^{20}\left(2^{20}+1\right)}{4^{15}\left(4^{10}+1\right)}=\dfrac{2^{20}+1}{4^{10}+1}\)
10 tháng 12 2017
T=\(\dfrac{45^{10}.5^{20}}{75^{15}}=\dfrac{9^{10}.5^{30}}{25^{15}.3^{15}}=\dfrac{3^{20}.5^{30}}{5^{30}.3^{15}}=3^5=243\)
1 tháng 7 2017
\(A=\dfrac{4\cdot5^{10}\cdot5^{10}}{75^{10}}=\dfrac{4\cdot5^{20}}{\left(3\cdot25\right)^{10}}=\dfrac{4\cdot5^{20}}{3^{10}\cdot25^{10}}=\dfrac{4\cdot5^{20}}{3^{10}\cdot\left(5^2\right)^{10}}=\dfrac{4\cdot5^{20}}{3^{10}\cdot5^{20}}=\dfrac{4}{3^{10}}\)
\(B=\dfrac{\left(0.8\right)^5}{\left(0.4\right)^6}=\dfrac{\left(\dfrac{4}{5}\right)^5}{\left(\dfrac{2}{5}\right)^6}=\dfrac{\left(2\cdot\dfrac{2}{5}\right)^5}{\left(\dfrac{2}{5}\right)^6}=\dfrac{2^5\cdot\left(\dfrac{2}{5}\right)^5}{\left(\dfrac{2}{5}\right)^5\cdot\dfrac{2}{5}}=\dfrac{2^5}{\dfrac{2}{5}}=2^5\cdot\dfrac{5}{2}=\dfrac{32\cdot5}{2}=80\)
\(C=\dfrac{2^{15}\cdot9^4}{6^6\cdot8^3}=\dfrac{2^{15}\cdot\left(3^2\right)^4}{\left(2\cdot3\right)^6\cdot\left(2^3\right)^3}=\dfrac{2^{15}\cdot3^8}{2^6\cdot3^6\cdot2^9}=\dfrac{2^{15}\cdot3^8}{2^6\cdot2^9}=\dfrac{2^{15}\cdot3^8}{2^{15}\cdot3^6}=\dfrac{3^8}{3^6}=3^2=9\)
\(D=\dfrac{8^{10}+4^{10}}{8^4+4^{11}}=\dfrac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\dfrac{2^{30}+2^{20}}{2^{12}+2^{22}}=\dfrac{2^{^{20}}\left(2^{10}+1\right)}{2^{12}\left(2^{10}+1\right)}=\dfrac{2^{20}}{2^{12}}=2^8=226\)
11 tháng 12 2017
a)\(\dfrac{6^6+6^3.3^3+3^6}{-73}\)\(=\dfrac{2^6.3^6+2^3.3^3.3^3+3^6}{-73}=\dfrac{2^6.3^6+2^3.3^6+3^6.1}{-73}\)
\(=\dfrac{3^6.\left(2^6+2^3+1\right)}{-73}=\dfrac{3^6\left(64+8+1\right)}{-73}=^{ }\)\(\dfrac{3^6.73}{-73}=\dfrac{3^6}{-1}=-3^6\)
b)\(\dfrac{8^{20}+4^{20}}{4^{25}+64^5}=\dfrac{2^{60}+2^{40}}{2^{50}+2^{30}}=\dfrac{2^{40}.\left(2^{20}+1\right)}{2^{30}.\left(2^{20}+1\right)}=\dfrac{2^{40}}{2^{30}}=2^{10}=1024\)
c)\(\dfrac{45^{10}.5^{20}}{75^{15}}=\dfrac{\left(3^2\right)^{10}.5^{10}.5^{20}}{\left(5^2\right)^{15}.3^{15}}=\dfrac{3^{20}.5^{30}}{5^{30}.3^{15}}=3^5=243\)
H9
HT.Phong (9A5)
CTVHS
22 tháng 7 2023
a) \(\dfrac{27^3\cdot11+9^5\cdot5}{3^9\cdot2^4}\)
\(=\dfrac{3^9\cdot11+3^{10}\cdot5}{3^9\cdot2^4}\)
\(=\dfrac{3^9\cdot\left(11+3\cdot5\right)}{3^9\cdot2^4}\)
\(=\dfrac{11+15}{16}\)
\(=\dfrac{26}{16}\)
\(=\dfrac{13}{8}\)
b) \(\dfrac{5^8+2^2\cdot25^4+2^3\cdot125^3-15^4\cdot5^4}{4^2\cdot625^2}\)
\(=\dfrac{5^8+2^2\cdot5^8+2^3\cdot5^9-3^4\cdot5^4\cdot5^4}{2^4\cdot5^8}\)
\(=\dfrac{5^8\cdot\left(1+2^2+2^3\cdot5-3^4\right)}{5^8\cdot2^4}\)
\(=\dfrac{1+4+40-81}{16}\)
\(=\dfrac{-36}{16}\)
\(=\dfrac{-9}{4}\)
c) \(\dfrac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}\)
\(=\dfrac{2^{10}\cdot3^8-2\cdot2^9\cdot3^9}{2^{10}\cdot3^8+2^{10}\cdot3^8\cdot5}\)
\(=\dfrac{2^{10}\cdot3^8\cdot\left(1-3\right)}{2^{10}\cdot3^8\cdot\left(1+5\right)}\)
\(=\dfrac{-2}{6}\)
\(=-\dfrac{1}{3}\)
TY
1
11 tháng 12 2022
\(N=\dfrac{3^6\cdot2^6+3^6\cdot2^3+3^6}{-73}=\dfrac{3^6\left(2^6+2^3+1\right)}{-73}=-3^6\)
\(T=\dfrac{5^{20}\cdot3^{20}}{5^{30}\cdot3^{15}}=\dfrac{3^5}{5^{10}}\)
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) \(\dfrac{ \left(x^2\right)^5}{\left(x^5\right)^2}=\dfrac{x^{10}}{x^{10}}=1\)
D
2
M
8 tháng 9 2018
\(\dfrac{45^{10}.5^{20}}{75^{15}}=\dfrac{\left(3^2\right)^{10}.5^{10}.5^{20}}{\left(5^2\right)^{15}.3^{15}}\dfrac{3^{20}.5^{30}}{5^{30}.3^{15}}=3^5\)
\(\dfrac{2^{15}.9^4}{6^6.8^3}=\dfrac{2^{15}.\left(3^2\right)^4}{2^3.3^3.\left(2^3\right)^3}=\dfrac{2^{15}.3^8}{2^3.3^3.2^9}=\dfrac{2^{15}.3^8}{2^{12}.3^3}\) =\(2^3.8^5\)
\(\dfrac{45^4.5^8}{75^6}=\dfrac{\left(5.9\right)^4.5^8}{\left(15.5\right)^6}=\dfrac{5^4.9^4.5^8}{15^6.5^6}=\dfrac{5^4.3^{2^4}.5^8}{\left(3.5\right)^6.5^6}=\dfrac{5^4.3^8.5^8}{3^6.5^6.5^6}=\dfrac{3^2.5^2}{5^2}=3^2=9\)
\(\dfrac{45^4.5^8}{75^6}=\dfrac{5^4.9^4.5^8}{3^6.5^6.5^6}=\dfrac{1.\left(3^2\right)^4.5^2}{3^6.5^2.1}=\dfrac{3^8.1}{3^6.1}=\dfrac{3^8}{3^6}=\dfrac{3^2}{1}=9\)