A/ 3^6.45^4-15^13.5^9/27^4.25^3+45^6 B/ 2/5^7.5^7+(9/4)^3:(3/16)^3/2^7.5^2+512

Đáp án:

$\begin{array}{l}
A = \dfrac{{{3^6}{{.45}^4} - {{15}^{13}}{{.5}^9}}}{{{{27}^4}{{.25}^3} + {{45}^6}}}\\
 = \dfrac{{{3^6}.{{\left( {{3^2}.5} \right)}^4} - {{\left( {3.5} \right)}^{13}}{{.5}^9}}}{{{{\left( {{3^3}} \right)}^4}.{{\left( {{5^2}} \right)}^3} + {{\left( {{3^2}.5} \right)}^6}}}\\
 = \dfrac{{{3^{14}}{{.5}^4} - {3^{13}}{{.5}^{22}}}}{{{3^{12}}{{.5}^6} + {3^{12}}{{.5}^6}}}\\
 = \dfrac{{{3^{13}}{{.5}^4}.\left( {3 - {5^{18}}} \right)}}{{{{2.3}^{12}}{{.5}^6}}}\\
 = \dfrac{{3.\left( {3 - {5^{18}}} \right)}}{{{{2.5}^2}}}\\
 = \dfrac{{9 - {{3.5}^{18}}}}{{50}}\\
b)\dfrac{2}{{{5^7}}}{.5^7} + {\left( {\dfrac{9}{4}} \right)^3}:\dfrac{{{{\left( {\dfrac{3}{{16}}} \right)}^3}}}{{{2^7}{{.5}^2}}} + 512\\
 = 2 + \dfrac{{{3^6}}}{{{2^6}}}.\dfrac{{{2^7}{{.5}^2}}}{{\dfrac{{{3^3}}}{{{{\left( {{2^4}} \right)}^3}}}}} + 512\\
 = 514 + \dfrac{{{3^6}}}{{{2^6}}}.\dfrac{{{2^7}{{.5}^2}{{.2}^{12}}}}{{{3^3}}}\\
 = 514 + {3^3}{.2^{13}}{.5^2}\\
 = 5530114
\end{array}$