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H9
HT.Phong (9A5)
CTVHS
15 tháng 10 2023
\(\dfrac{27^{10}+9^5}{9^{13}+27^2}\)
\(=\dfrac{\left(3^3\right)^{10}+\left(3^2\right)^5}{\left(3^2\right)^{13}+\left(3^3\right)^2}\)
\(=\dfrac{3^{30}+3^{10}}{3^{26}+3^6}\)
\(=\dfrac{3^{10}\cdot\left(3^{20}+1\right)}{3^6\cdot\left(3^{20}+1\right)}\)
\(=\dfrac{3^{10}}{3^6}\)
\(=3^{10-6}\)
\(=3^4\)
26 tháng 8 2018
3. Từ \(\dfrac{x-2}{27}=\dfrac{3}{x-2}\Rightarrow\left(x-2\right)^2=81\)
\(\Rightarrow\left(x-2\right)^2=\left(\pm9\right)^2\\ \Rightarrow\left[{}\begin{matrix}x-2=-9\\x-2=9\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-7\\x=11\end{matrix}\right.\)
Vậy x = -7 hoặc x = 11
4. Từ \(\dfrac{2x+5}{9-2x}=\dfrac{2}{5}\)
\(\Rightarrow5\left(2x+5\right)=2\left(9-2x\right)\\ \Leftrightarrow10x+25=18-4x\\ \Leftrightarrow14x=-7\\ \Rightarrow x=-\dfrac{1}{2}\)
5. Từ \(\dfrac{x-7}{x+8}=\dfrac{x-8}{x+9}\)
\(\Rightarrow\left(x-7\right)\left(x+9\right)=\left(x-8\right)\left(x+8\right)\\ \Leftrightarrow x^2+2x-63=x^2-64\\ \Leftrightarrow2x=-1\\ \Rightarrow x=-\dfrac{1}{2}\)
MV
29 tháng 10 2017
\(A=\dfrac{12^{15}\cdot3^4-4^5\cdot3^9}{27^3\cdot2^{10}-32^3\cdot3^9}\\ =\dfrac{\left(2^2\cdot3\right)^{15}\cdot3^4-\left(2^2\right)^5\cdot3^9}{\left(3^3\right)^3\cdot2^{10}-\left(2^5\right)^3\cdot3^9}\\ =\dfrac{2^{30}\cdot3^{15}\cdot3^4-2^{10}\cdot3^9}{3^9\cdot2^{10}-2^{15}\cdot3^9}\\ =\dfrac{3^9\cdot2^{10}\left(2^{20}\cdot3^{10}\right)}{3^9\cdot2^{10}\left(1-2^5\right)}\\ =\dfrac{\left(2^2\right)^{10}\cdot3^{10}}{1-32}\\ =\dfrac{\left(2^2\cdot3\right)^{10}}{-31}\\ =\dfrac{-12^{10}}{31}\)
\(B=\dfrac{3}{1^2\cdot2^2}+\dfrac{5}{2^2\cdot3^2}+...+\dfrac{99}{49^2\cdot50^2}\\ =\dfrac{2^2-1^2}{1^2\cdot2^2}+\dfrac{3^2-2^2}{2^2\cdot3^2}+...+\dfrac{50^2-49^2}{49^2\cdot50^2}\\ =\dfrac{1}{1^2}-\dfrac{1}{2^2}+\dfrac{1}{2^2}-\dfrac{1}{3^2}+...+\dfrac{1}{49^2}-\dfrac{1}{50^2}\\ =1-\dfrac{1}{2500}\\ =\dfrac{2499}{2500}\)
S
25 tháng 12 2017
a, \(5\dfrac{4}{13}.15\dfrac{3}{41}-5\dfrac{4}{13}.2\dfrac{3}{41}\)
\(=\left(15\dfrac{3}{41}-2\dfrac{3}{41}\right).\dfrac{69}{13}=\dfrac{13.69}{13}=69\)
b, \(\dfrac{2^3}{3^3}:\dfrac{16}{27}+\dfrac{2017}{2018}-\dfrac{1}{2}.2017^0\)
\(=\dfrac{8}{27}:\dfrac{16}{27}+\dfrac{2017}{2018}-\dfrac{1}{2}.1=\dfrac{1}{2}+\dfrac{2017}{2018}-\dfrac{1}{2}=\dfrac{2017}{2018}\)
c, \(3:\left(-\dfrac{3}{2}\right)^2+\dfrac{1}{9}.\sqrt{36}=3:\dfrac{9}{4}+\dfrac{1}{9}.6=\dfrac{4}{3}+\dfrac{2}{3}=\dfrac{6}{3}=2\)
NT
1
2 tháng 10 2018
\(\dfrac{2^{30}.5^7+2^{13}.5^{27}}{2^{27}.5^7+2^{10}.5^{27}}=\dfrac{2^{13}.5^7.\left(2^{17}+5^{20}\right)}{2^{10}.5^7.\left(2^{17}+5^{20}\right)}= \dfrac{2^{13}.5^7}{2^{10}.5^7}=2^3=8\)
9 tháng 6 2022
a: a/3=b/5
nên a/9=b/15
b/3=c/2
nên b/15=c/10
=>a/9=b/15=c/10
Áp dụng tính chất của dãy tỉ số bằg nhau, ta được:
\(\dfrac{a}{9}=\dfrac{b}{15}=\dfrac{c}{10}=\dfrac{a+b+c}{9+15+10}=\dfrac{27}{34}\)
Do đó: a=243/34; b=405/34; c=270/34
b: Áp dụng tính chất của dãy tỉ số bằng nhau, ta được
\(\dfrac{x}{\dfrac{5}{2}}=\dfrac{y}{9}=\dfrac{z}{7}=\dfrac{y-z}{9-7}=\dfrac{10}{2}=5\)
Do đó x=25/4; y=45; z=35
TP
1
24 tháng 5 2022
\(=\dfrac{3^6\cdot\left(3^2\right)^4\cdot5^4-5^{13}\cdot3^{13}\cdot5^{-9}}{3^{12}\cdot5^6+\left(3^2\right)^6\cdot5^6}\)
\(=\dfrac{3^{14}\cdot5^4-5^4\cdot3^{13}}{3^{12}\cdot5^6+3^{12}\cdot5^6}=\dfrac{3^{13}\cdot5^4\cdot2}{2\cdot3^{12}\cdot5^6}=\dfrac{3}{5^2}=\dfrac{3}{25}\)
5 tháng 8 2018
tử số=3^6.45^4-15^13.5^-9=3^6.(5.3^2)^4-(3.5)^13.5^-9=3^6.5^4.3^8-3^13.5^13.5^-9=3^14.5^4-3^13.5^4(3-1)=2.3^13.5^4
mẫu số=27^4.25^3+45^6=3^12.5^6+3^12.5^6=2.3^12.5^6
phân số =(2.3^13.5^4)/2.3^12.5^6=3/25
\(A=\dfrac{27^{10}+9^5}{9^{13}+27^2}\\ =\dfrac{\left(3^3\right)^{10}+\left(3^2\right)^5}{\left(3^2\right)^{13}+\left(3^3\right)^2}\\ =\dfrac{3^{30}+3^{10}}{3^{26}+3^6}\\ =\dfrac{3^{10}\left(3^{20}+1\right)}{3^6\left(3^{20}+1\right)}\\ =\dfrac{3^{10}}{3^6}\\=3^4\\ =81\)
\(A=\dfrac{27^{10}+9^5}{9^{13}+27^2}\)
\(A=\dfrac{\left(3^3\right)^{10}+\left(3^2\right)^5}{\left(3^2\right)^{13}+\left(3^3\right)^2}\)
\(A=\dfrac{3^{30}+3^{10}}{3^{26}+3^6}\)
\(A=\dfrac{3^{10}+\left(3^{20}+1\right)}{3^6.\left(3^{20}+1\right)}\)
\(A=\dfrac{3^{10}}{3^6}\)
\(A=3^4\)
\(A=81\)