Question

Rút gọn 

 B = \(\frac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)

 

Answer 1

\(\frac{3^6\times45^4-15^{13}\times5^{-9}}{27^4\times25^3+45^6}\)

\(=\frac{3^6\times\left(3^2\times5\right)^4-\left(3\times5\right)^{13}\times5^{-9}}{\left(3^3\right)^4\times\left(5^2\right)^3+\left(3^2\times5\right)^6}\)

\(=\frac{3^6\times3^8\times5^4-3^{13}\times5^{13}\times5^{-9}}{3^{12}\times5^6+3^{12}\times5^6}\)

\(=\frac{3^{14}\times5^4-3^{13}\times5^4}{3^{12}\times5^6+3^{12}\times5^6}\)

\(=\frac{3^{13}\times5^4\times\left(3-1\right)}{2\times3^{12}\times5^6}\)

\(=\frac{3\times2}{2\times5^2}\)

\(=\frac{3}{25}\)

Answer 2

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