\(\frac{1}{y}-\frac{2}{x}=\frac{7}{y}\)

\(\frac{2}{x}=\frac{1}{y}-\frac{7}{y}\)

\(\frac{2}{x}=\frac{1-7}{y}\)

\(2y=6x\)

8⁴.16⁵=2³²

5⁴⁰.125².25³=5⁵²

27⁴.81¹⁰=3⁵²

10³.100⁵.1000⁴=10²⁵

Chúc hk tốt!!!

+) \(8^4\times16^5=\left(2^3\right)^4\times\left(2^4\right)^5=2^{12}\times2^{20}=2^{12+20}=2^{32}\)

+) \(5^{40}\times125^2\times25^3=5^{40}\times\left(5^3\right)^2\times\left(5^2\right)^3=5^{40}\times5^6\times5^6=5^{40+6+6}=5^{52}\)

+) \(27^4\times81^{10}=\left(3^3\right)^4\times\left(3^4\right)^{10}=3^{12}\times3^{40}=3^{12+40}=3^{52}\)

+) \(10^3\times100^5\times1000^4=10^3\times\left(10^2\right)^5\times\left(10^3\right)^4=10^3\times10^{10}\times10^{12}=10^{3+10+12}=10^{25}\)

_Chúc bạn học tốt_

\(\left(7x-15\right):3=2\)

\(7x-15=2.3\)

\(7x-15=6\)

\(7x=6+15\)

\(7x=21\)

\(x=\frac{21}{7}\)

\(x=3\)

Vậy \(x=3\)

7x-15=6

7x=21

x=3

\(a,\overline{abcabc}=\overline{abc}.1001\)

Nên không đủ điều kiện để chứng minh.

\(b,\overline{aaaaa}=a.11111\)

Do \(11111⋮7\)

\(\Rightarrow a.11111⋮7\Leftrightarrow\overline{aaaaa}⋮7\left(đpcm\right).\)

\(A=2.4.8.16.256=2.2^2.2^3.2^4.2^8=2^{18}\)

\(B=3.9.27.81.729=3.3^2.3^3.3^4.3^6=3^{16}\)

\(C=5.25.125.625.5^7=5.5^2.5^3.5^4.5^7=5^{17}\)

\(D=7.49.343.7^7=7.7^2.7^3.7^7=7^{13}\)

A = 2.4.8.16.256

A = 2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2

A = 2¹⁸