Question

[Lương Khánh Huyền]

10.[(4⁶.9⁵-6⁹.120) :(8⁴.3¹²-6¹¹)]  ( đưa về cơ số 6 nha )

Answer 1

[soyeon_Tiểubàng giải]

\(\frac{10.\left(4^6.9^5-6^9.120\right)}{8^4.3^{12}-6^{11}}=\frac{10.4^6.9^5-10.6^9.120}{\left(2^3\right)^4.3^{12}-6^{11}}=\frac{2.5.\left(2^2\right)^6.\left(3^2\right)^5-2.5.6^9.2^3.3.5}{2^{12}.3^{12}-6^{11}}\)

\(=\frac{2.5.2^{12}.3^{10}-2^4.3.5^2.6^9}{6^{12}-6^{11}}=\frac{2^{13}.5.3^{10}-6.2^3.5^2.6^9}{6^{11}.\left(6-1\right)}\)

\(=\frac{6^{10}.2^3.5-6^{10}.2^3.5^2}{6^{11}.5}=\frac{6^{10}.2^3.5.\left(1-5\right)}{6^{11}.5}\)

\(=\frac{2^3.\left(-4\right)}{6}=\frac{8.\left(-4\right)}{6}=\frac{-32}{6}=\frac{-16}{3}\)