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Đặt \(A=\frac{2^{19}\cdot27^3+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\)
\(A=\frac{2^{19}\cdot\left(3^3\right)^3+15\cdot\left(2^2\right)^9\cdot\left(3^2\right)^4}{6^9\cdot2^9\cdot2+12^{10}}\)
\(A=\frac{2^{19}\cdot3^9+15\cdot2^{18}\cdot3^8}{12^9\cdot2+12^9\cdot12}=\frac{\left(2^{18}\cdot3^8\right)\cdot6+\left(2^{18}\cdot3^8\right)\cdot15}{12^9\cdot\left(2+12\right)}\)
\(A=\frac{\left(2^{18}\cdot3^8\right)\cdot\left(6+15\right)}{12^9\cdot14}=\frac{2^{18}\cdot3^8\cdot21}{12^9\cdot14}=\frac{2^{18}\cdot3^8\cdot7\cdot3}{2^{18}\cdot3^9\cdot7\cdot2}=\frac{3^8\cdot3}{3^8\cdot3\cdot2}\)
\(A=\frac{1}{2}\)
Đặt \(B=\frac{4}{35}+\frac{4}{63}+\frac{4}{99}+\frac{4}{143}+\frac{4}{195}=\frac{4}{5\cdot7}+\frac{4}{7\cdot9}+\frac{4}{9\cdot11}+\frac{4}{11\cdot13}+\frac{4}{13\cdot15}\)
\(B=\frac{1}{2}\left(\frac{4}{5}-\frac{4}{7}+\frac{4}{7}-\frac{4}{9}+...+\frac{4}{13}-\frac{4}{15}\right)\)
\(B=\frac{1}{2}\left(\frac{4}{5}-\frac{4}{15}\right)\)mà \(\frac{4}{5}-\frac{4}{15}< 1\Leftrightarrow\frac{1}{2}\left(\frac{4}{5}-\frac{4}{15}\right)< \frac{1}{2}\Leftrightarrow B< A\)
\(a,\left(-2\right)^{300}=2^{300}=\left(2^3\right)^{100}=8^{100}\)
\(\left(-3\right)^{200}=3^{200}=\left(3^2\right)^{100}=9^{100}\)
\(\Leftrightarrow\left(-3\right)^{200}>\left(-2\right)^{300}\)
\(b,A=2^{19}.27^3+15.4^9.9^4\)
\(\frac{2^{19}\times27^3+15\times4^9\times9^4}{6^9\times2^{10}+12^{10}}\)
\(=\frac{2^{19}\times\left(3^3\right)^3+5\times3\times\left(2^2\right)^9\times\left(3^2\right)^4}{\left(2\times3\right)^9\times2^{10}+\left(3\times4\right)^{10}}\)
\(=\frac{2^{19}\times3^9+3\times5\times2^{18}\times3^8}{3^9\times2^9\times2^{10}+3^{10}\times4^{10}}\)
\(=\frac{2^{19}\times3^9+5\times2^{18}\times3^9}{3^9\times2^{19}+3^{10}\times\left(2^2\right)^{10}}\)
\(=\frac{2^{18}\times3^9\times\left(2+5\right)}{3^9\times2^{19}+3^{10}\times2^{20}}\)
\(=\frac{2^{18}\times3^9\times7}{2^{19}\times3^9\times\left(1+3\times2\right)}\)
\(=\frac{7}{2\times\left(1+6\right)}\)
\(=\frac{7}{2\times7}\)
\(=\frac{1}{2}\)
A = 2^19.27^3+15.4^9.9^4 / 6^9.2^10+12^10
= 2^19.3^9 + 5.2^18.3^9 / 3^9.2^19 + 2^20.3^10
= 2^18.3^9 ( 2 + 5 ) / 2^19.3^9.(1 + 2.3)
= (2 + 5) / 2(1 + 6)
= 7 / 2.7
= 1/2
\(=\dfrac{2^{19}\cdot3^9+2^{18}\cdot3^9\cdot5}{2^{19}\cdot3^9+2^{20}\cdot3^{10}}=\dfrac{2^{18}\cdot3^9\cdot\left(2+5\right)}{2^{19}\cdot3^9\cdot7}=\dfrac{1}{2}\)
A=2^19.3^9+3.5.2^18.3^8/3^9.2^9.2^10+3^10.2^20.
A=2^18.3^9.2+3^9.2^18.5/3^9.2^18.2+3^9.
A=3^9.2^18.(2+5)/3^9.2^18.(2+3.2^2).
A=7/14.
A=1/2.
BÀI 2
60%.x + 0,4.x + x:3= 2
\(\frac{60}{100}\)x + \(\frac{4}{10}\).x + x. \(\frac{1}{3}\)=2
\(\frac{3}{5}\).x + \(\frac{2}{5}\).x + x.\(\frac{1}{3}\)=2
(\(\frac{3}{5}\)+ \(\frac{2}{5}\)+ \(\frac{1}{3}\)) .x =2
\(\frac{4}{3}\).x =2
x = 2: \(\frac{4}{3}\)
x = \(\frac{3}{2}\)
Vậy x=\(\frac{3}{2}\)
k cho mik nha các bạn
Bài 2 :
60%x + 0.4x + x : 3 = 2
\(x.\left(\frac{60}{100}+\frac{2}{5}+\frac{1}{3}\right)\)= 2
\(x.\frac{4}{3}\)= 2
\(x=2.\frac{3}{4}\)
\(x=1.5\)