Question

Rút gọn

C = \(\frac{\left(\frac{2}{5}\right)^7.5^7+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7.5^2+512}\)

Answer 1

\(C=\frac{\left(\frac{2}{5}\right)^7\times5^7+\left(\frac{9}{4}\right)^3\div\left(\frac{3}{16}\right)^3}{2^7\times5^2+512}\)

\(=\frac{\left(\frac{2}{5}\times5\right)^7+\left(\frac{9}{4}\div\frac{3}{16}\right)^3}{2^7\times5^2+2^9}\)

\(=\frac{2^7+12^3}{2^7\times\left(25+2^2\right)}\)

\(=\frac{2^7+\left(2^2\times3\right)^3}{2^7\times\left(25+4\right)}\)

\(=\frac{2^7+2^6\times3^3}{2^7\times29}\)

\(=\frac{2^6\times\left(2+27\right)}{2^7\times29}\)

\(=\frac{29}{2\times29}\)

\(=\frac{1}{2}\)