Question

Find the value of $\frac{(2^{19}\times {27}^3)+(15\times 4^9\times 9^4)}{(6^9\times 2^{10})+{12}^{10}}$

Answer 1

$Now\frac{(2^{19}\times {27}^3)+(15\times 4^9\times 9^4)}{(6^9\times 2^{10})+{12}^{10}}\to \frac{(2^{19}\times {\left(3^3\right)}^3)+(3\times 5\times {\left(2^2\right)}^9\times {\left(3^2\right)}^4)}{({(2\times 3)}^9\times 2^{10})+{(2^2\times 3)}^{10}}\to \frac{(2^{19}\times 3^9)+(3\times 5\times 2^{18}\times 3^8)}{(2^9\times 3^9\times 2^{10})+{\left(2^2\right)}^{10}{3}^{10}}\to \frac{(2^{19}\times 3^9)+(5\times 2^{18}\times 3^{8+1})}{(3^9\times 2^{10+9})+2^{20}{\times 3}^{10}}\to \frac{(2^{19}\times 3^9)+(5\times 2^{18}\times 3^9)}{(3^9\times 2^{19})+2^{20}{\times 3}^{10}}\to \frac{(2^{19}\times 3^9)+(5\times 2^{19-1}\times 3^9)}{(3^9\times 2^{19})+2^{19+1}{\times 3}^{9+1}}\to \frac{(2^{19}\times 3^9)+(5\times \frac{2^{19}}{2}\times 3^9)}{(3^9\times 2^{19})+2^{19}\times 2^1{\times 3}^9\times 3^1}\to \frac{(2^{19}\times 3^9)}{(2^{19}\times 3^9)}\times \left(\frac{1+\left(\frac{5}{2}\right)}{1+2\times 3}\right)\to 1\times \left(\frac{\frac{2+5}{2}}{1+6}\right)\to \frac{\frac{7}{2}}{7}=\frac{1}{2}=0.50$