Question

[Đặng Vũ Phương Thảo]

Mong các bạn trả lời nhanh vì mình đang cần gấp!

Bài 1:

\(\frac{3^{2014}.8^{19}}{6^{60}.3^{1955}}\)

Bài 2:

\(5^x+5^{x+1}=150\)

Bài 3:

\(A=\frac{3}{11.16}+\frac{3}{16.21}+\frac{3}{21.26}+....+\frac{3}{61.66}\)

Cảm ơn rất nhìu!  ^_^

Answer 1

[Xyz OLM]

1) \(\frac{3^{2014}.8^{19}}{6^{60}.3^{1955}}=\frac{3^{2014}.\left(2^3\right)^{19}}{\left(2.3\right)^{60}.3^{1955}}=\frac{3^{2014}.2^{57}}{2^{60}.3^{2015}}=\frac{1}{2^3.3}=\frac{1}{24}\)

2) \(5^x+5^{x+1}=150\)

=> 5^x(1 + 5) = 150

=> 5^x.6 = 150

=> 5^x = 25

=> \(x=\pm2\)

3) \(\frac{3}{11.16}+\frac{3}{16.21}+...+\frac{3}{61.66}=\frac{3}{5}\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)\)

\(=\frac{3}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)=\frac{3}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)=\frac{3}{5}.\frac{5}{66}=\frac{1}{22}\)

Answer 2

[Đặng Vũ Phương Thảo]

cảm ơn bạn Xyz đã trả lời