Question

Tính A

A=\(\dfrac{3^6\cdot45^4-15^{13}\cdot\left(\dfrac{1}{5}\right)^9}{27^4\cdot25^3+45^6}\)

Answer 1

\(A=\dfrac{3^6.45^4-15^{13}.\left(\dfrac{1}{5}\right)^9}{27^4.25^3+45^6}\)

\(=\dfrac{3^6.3^8.5^4-5^{13}.3^{13}.\left(\dfrac{1}{5}\right)^9}{3^{12}.5^6+3^{12}.5^6}\)

\(=\dfrac{3^{14}.5^4-5^{13}.3^{13}.\left(\dfrac{1}{5}\right)^9}{3^{12}.5^6+3^{12}.5^6}\)

\(=\dfrac{3^{13}\left[3.5^4-5^{13}.\left(\dfrac{1}{5}\right)^9\right]}{3^{12}(5^6+5^6)}\)

\(=\dfrac{3^{13}.1250}{3^{12}.31250}\)

\(=\dfrac{3^{13}.5^4.2}{3^{12}.5^6.2}\)

\(=\dfrac{3}{5^2}=\dfrac{3}{25}\)

Vậy \(A=\dfrac{3}{25}\)