\(M=\frac{8^{20}+4^{20}}{4^{25}+64^5}\)
\(=\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}\)
\(=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}\)
\(=\frac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}\)
\(=2^{10}=1024\)
#)Giải :
\(M=\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}=\frac{2^{40}.2^{20}+2^{40}.1}{2^{30}.2^{20}+2^{30}.1}=\frac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}=\frac{2^{40}}{2^{30}}=2^{10}=1024\)
Ta có 1 cách đơn giản và easy hơn
\(\frac{4^{20}\left(2^{20}+1\right)}{4^{15}+4^{10}+1}=1024\)
\(M=\frac{8^{20}+4^{20}}{4^{25}+64^5}\)
\(=\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}\)
\(=\frac{2^{3.20}+2^{2.20}}{2^{2.25}+2^{6.5}}\)
\(=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}\)
\(=\frac{2^{6.10}+2^{4.10}}{2^{5.10}+2^{3.10}}\)
\(=\frac{2^6.2^{10}+2^4.2^{10}}{2^5.2^{10}+2^3.2^{10}}\)
\(=\frac{2^{10}.\left(2^6+2^4\right)}{2^{10}.\left(2^5+2^3\right)}\)
\(=\frac{2^{10}.\left(64+16\right)}{2^{10}.\left(32+8\right)}\)
\(=\frac{2^{10}.80}{2^{10}.40}\)
\(=\frac{2^{10}.40.2}{2^{10}.40}\)
\(=2\)
Lưu ý : Dấu "." là dấu nhân
