Question

Thực hiện phép tính:

\(\frac{1+2.3^6}{2^3.3^6-2^3.5^3}-\frac{1+3^6}{8.\left(9^3-125\right)}-\frac{5^3}{18^3-10^3}\)

Answer 1

\(\frac{1+2.3^6}{2^3.3^6-2^3.5^3}-\frac{1+3^6}{8\left(9^3-125\right)}-\frac{5^3}{18^3-10^3}\)

\(=\frac{1+2.3^6}{2^3\left(3^6-5^5\right)}-\frac{1+3^6}{2^3\left[\left(3^2\right)^3-5^3\right]}-\frac{5^3}{\left(2.3^2\right)^3-\left(2.5\right)^3}\)

\(=\frac{1+2.3^6}{2^3\left(3^6-5^3\right)}-\frac{1+3^6}{2^3\left(3^6-5^3\right)}-\frac{5^3}{2^3\left(3^6-5^3\right)}\)

\(=\frac{\left(1+2.3^6\right)-\left(1+3^6\right)-5^3}{2^3\left(3^6-5^2\right)}\)

\(=\frac{3^6-5^3}{2^3\left(3^6-5^3\right)}\)

\(=\frac{1}{8}\)