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a, 2 x 14 x 12 + 4 x 6 x 21 + 8 x 3 x 62
= 24 x 14 + 24 x 21 + 24 x 62
= 24 x ( 14 + 21 + 62 )
= 24 x 97
= 21 x ( 97 + 3 )
= 21 x 100
= 2100
b, và c, ( Tương tự câu a, )
\(\dfrac{5\times4^{15}\times9^9-4\times3^{20}\times8^9}{5\times2^{10}\times6^{19}-7\times2^{29}\times27^6}\\ =\dfrac{5\times2^{30}\times3^{18}-2^2\times3^{20}\times2^{27}}{5\times2^{10}\times3^{19}\times2^{19}-7\times2^{29}\times3^{18}}\\ =\dfrac{5\times2^{30}\times3^{18}-2^{29}\times3^{20}}{5\times2^{29}\times3^{19}-7\times2^{29}\times3^{18}}\\ =\dfrac{2^{29}\times3^{18}\times\left(5\times2-3^2\right)}{2^{29}\times3^{18}\times\left(5\times3-7\right)}\\ =\dfrac{10-9}{15-7}\\ =\dfrac{1}{8}\)
\(A=1+2+2^2+2^3+2^4+...+2^{49}\)
\(2A=2+2^2+2^3+2^4+..+2^{50}\)
\(2A-A=\left(2+2^2+2^3+2^2+...+2^{50}\right)-\left(1+2+2^2+2^3+...+2^{49}\right)\)
\(\Rightarrow A=2^{50}-1\)
\(a)\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}=\frac{-5}{3^2}=\frac{-5}{9}\)
\(b)\frac{-11.13^7}{11^5.13^8}=\frac{-1}{11^4.13}\) (Bạn xem thử xem có sai đề không nhé)
\(c)\frac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}=\frac{2^{10}.3^9\left(3+1\right)}{2^9.3^{10}}=\frac{2.4}{3}=\frac{8}{3}\)
\(d)\frac{5^{11}.7^{12}+5^{11}.7^{11}}{5^{12}.7^{12}+9.5^{11}.7^{11}}=\frac{5^{11}.7^{11}\left(7+1\right)}{5^{11}.7^{11}\left(5.4+9\right)}=\frac{8}{20+9}=\frac{8}{29}\)
\(a)\frac{3^{10}\cdot\left(-5\right)^{21}}{\left(-5\right)^{20}\cdot3^{12}}=\frac{-5}{3^2}=\frac{-5}{9}\)
\(b)\frac{\left(-11\right)\cdot13^7}{11^5\cdot13^8}=\frac{-1}{11^4\cdot13}=\frac{-1}{14641\cdot13}=\frac{-1}{190333}\)
\(c)\frac{2^{10}\cdot3^{10}-2^{10}\cdot3^9}{2^9\cdot3^{10}}=\frac{2^{10}\left(3^{10}-3^9\right)}{2^9\cdot3^{10}}=\frac{2^{10}\cdot3^9\left(3-1\right)}{2^9\cdot3^{10}}=\frac{2^{10}\cdot3^9\cdot2}{2^9\cdot3^{10}}=\frac{2\cdot2}{3}=\frac{4}{3}\)
\(A=\frac{15.3^{11}+4.27^4}{9^7}=\frac{3.5.3^{11}+2^2.\left(3^3\right)^4}{\left(3^2\right)^7}=\frac{3^{12}.5+2^2.3^{12}}{3^{14}}\)
\(=\frac{3^{12}\left(5+4\right)}{3^{14}}=\frac{3^{12}.9}{3^{14}}\)
\(=\frac{3^{12}.3^2}{3^{14}}=\frac{3^{14}}{3^{14}}=1\)
Vậy giá trị biểu thức A là 1.
\(A=\frac{15.3^{11}+4.27^4}{9^7}\)
\(=\frac{3.5.3^{11}+4.3^{3.4}}{3^{2.7}}=\frac{3^{12}.5+3^{12}.4}{3^{14}}=\frac{3^{12}.5+4}{3^{14}}\)
\(=\frac{9}{3^2}=\frac{9}{9}=1\)
Vậy Giá trị biểu thức là 1
3^x = 3^3.3^5
3^x = 3^ (5 +3)
3^x = 3^5
=> x = 5
2, 2^x = 4 .128
2^x = 2^2 . 2^7
2^x = 2^ ( 2 +7)
2^x = 2^9
=> x = 9
3, 2^x.3^x = 2^2 . 3^2
=> x = 2
ta co
\(2\times3^x=10\times3^{12}+8\times27^4\)
\(\Leftrightarrow2\times3^x=10\times3^{12}+8\times3^{12}\)
\(\Leftrightarrow2\times3^x=3^{12}\times18\)
\(\Leftrightarrow2\times3^x=2\times3^{14}\)
\(\Leftrightarrow x=14\)