thank you

mình đc 1/6 này.

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vậy 1/6 của bn chắc là đúng rồi, vì lp mik nhiều bn làm như vậy hơn

\(A=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^6\cdot3^3+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot2^3}\)

\(=\dfrac{2^{12}\cdot3^4\cdot\left(3-1\right)}{2^6\cdot3^3\cdot\left(1+2^6\cdot3^2\right)}-\dfrac{5^{10}\cdot7^3\cdot\left(1-7\right)}{5^9\cdot7^3\cdot\left(1+2^3\right)}\)

\(=\dfrac{2^6\cdot3\cdot2}{1+64\cdot9}-\dfrac{5\cdot\left(-6\right)}{9}\)

\(=\dfrac{2^7\cdot3}{1+576}+\dfrac{30}{9}\)

\(=\dfrac{384}{577}+\dfrac{30}{9}=\dfrac{384}{577}+\dfrac{10}{3}=\dfrac{6922}{1731}\)

\(A=\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)

\(=\dfrac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\dfrac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)

\(=\dfrac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5.\left(3+1\right)}-\dfrac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3.\left(1+2^3\right)}\)

\(=\dfrac{2^{12}.3^4.2}{2^{12}.3^5.4}-\dfrac{5^{10}.7^3.\left(-6\right)}{5^9.7^3.9}\)

\(=\dfrac{1}{6}-\dfrac{-10}{3}\)

\(=\dfrac{7}{2}\)

hack não qué

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

16⁵ : 8⁵ = (2⁴)⁵ : (2³)⁵

             = 2²⁰ : 2¹⁵ 

             = 2⁵

câu b thôi nha

16^15=8^30

8^30:8^5=8^25

1. \(\left(-\dfrac{3}{2}\right)^2=\dfrac{9}{4}\)

\(\Rightarrow\left(-\dfrac{3}{2}\right)^x=\left(-\dfrac{3}{2}\right)^2\)

\(\Rightarrow x=2\)

2.\(3^{2x+2}=9^{10}\)

\(\Rightarrow3^{2x+2}=\left(3^2\right)^{10}\)

\(\Rightarrow3^{2x+2}=3^{20}\)

\(\Rightarrow2x+2=20\)

\(\Rightarrow2x=18\)

\(\Rightarrow x=9\)

3)\(3^{3-2x}=27^{13}\)

\(\Rightarrow3^{3-2x}=\left(3^3\right)^{13}\)

\(\Rightarrow3^{3-2x}=3^{39}\)

\(\Rightarrow3-2x=39\)

\(\Rightarrow2x=-36\)

\(\Rightarrow x=-18\)

4)\(5.3^x=7.3^5-2.3^5\)

\(\Rightarrow5.3^x=3^5\left(7-2\right)\)

\(\Rightarrow5.3^x=3^5.5\)

\(\Rightarrow3^x=3^5\)

\(\Rightarrow x=5\)

M=\(\dfrac{3}{1^2.2^2}+\dfrac{5}{2^2.3^2}+\dfrac{7}{3^2.4^2}+...+\dfrac{17}{8^2.9^2}+\dfrac{19}{9^2.10^2}\)

=\(\dfrac{3}{1.4}+\dfrac{5}{4.9}+\dfrac{7}{9.16}+...+\dfrac{17}{64.81}+\dfrac{19}{81.100}\)

=\(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+...+\dfrac{1}{64}-\dfrac{1}{81}+\dfrac{1}{81}-\dfrac{1}{100}\)

=1-\(\dfrac{1}{100}\)=\(\dfrac{99}{100}\)<\(\dfrac{100}{100}=1\)

.

1) \(7.4^x=7.4^3\Leftrightarrow4^x=4^3;x=3\)

2) \(\frac{3}{2.5^x}=\frac{3}{2.5^{12}}\Leftrightarrow5^x=5^{12};x=12\)

\(2^x=2.2^8=2^9;x=9\)

4) \(5.3^x=7.3^5-2.3^5\Leftrightarrow5.3^x=3^5.\left(7-2\right)\)

\(\Leftrightarrow3^5.x=3^5.5;x=5\)