Question

[Dương Thanh Hương]

Tính;

A= 2^12.3^5-4^6.9^2/(2^2.3)^6 - 5^10.7^3-25^5.49^2/(125.7)^3+5^9.14^3

Answer 1

[Nguyễn Lê Phước Thịnh]

Ta có: \(\frac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6}\)

\(=\frac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6}=\frac{2^{12}\cdot3^4\left(3-1\right)}{2^{12}\cdot3^6}\)

\(=\frac{3^4\cdot2}{3^6}=\frac{2}{3^2}=\frac29\)

Ta có: \(\frac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)

\(=\frac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot2^3}\)

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

Ta có: \(A=\frac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6}-\frac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)

\(=\frac29+\frac{10}{3}=\frac29+\frac{30}{9}=\frac{32}{9}\)