\(M=\frac{8^{20}+4^{20}}{4^{25}+64^5}\)

\(M=\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}\)

\(M=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}\)

\(M=\frac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}\)

\(M=2^{10}\)

\(M=1024\)

\(M=\frac{8^{20}+4^{20}}{4^{25}+64^5}=\frac{4^{20}.\left(2^{20}+1\right)}{4^{25}+\left(4^3\right)^5}=\frac{4^{20}.\left(2^{20}+1\right)}{4^{25}+4^{15}}\)

                                                                      \(=\frac{4^{20}.\left(4^{10}+1\right)}{4^{25}.\left(4^{10}+1\right)}=\frac{1}{4^5}=\frac{1}{1024}\)

\(\frac{8^{20}+4^{20}}{4^{25}+64^5}=\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}=\frac{2^{40}\times\left(2^{20}+1\right)}{2^{30}\times\left(2^{20}+1\right)}=2^{10}=1024\)

Chúc bạn học tốt ^^

\(M=\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}=\frac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}=2^{10}\)

\(M=\frac{8^{20}+4^{20}}{4^{25}+64^5}\)

     = \(\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}=\frac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}=2^{10}\)

 \(M=\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)+\left(2^6\right)^5}\)

\(M=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}\)

\(M=\frac{2^{40}\cdot2^{20}+2^{40}\cdot1}{2^{30}\cdot2^{20}+2^{30}\cdot1}\)

\(M=\frac{2^{40}\cdot\left(2^{20}+1\right)}{2^{30}\cdot\left(2^{20}+1\right)}\)

\(M=\frac{2^{40}}{2^{30}}\)

\(M=2^{40-30}\)

\(M=2^{10}\)

\(M=1024\)

M=8²⁰ +4²⁰/4²⁵+64⁵

M=(2³)²⁰+(2²)²⁰/(2²)²⁵+(2⁵)⁵

M=2⁶⁰+2⁴⁰/2⁵⁰+2²⁵

M=2²⁵(2³⁵+2¹⁵)/2²⁵(2²⁵+1)

M=2³⁵+2¹⁵/2²⁵+1

\(\frac{8^{20}+4^{20}}{4^{25}+64^5}\)=\(\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}\)=\(\frac{2^{60}+2^{40}}{2^{50}+2^{30}}\)=\(\frac{2^{100}}{2^{80}}\)=2²⁰

\(M=\frac{8^{20}+4^{20}}{4^{25}+64^5}\)

      \(=\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}\)

       \(=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}\)

       \(=\frac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}\)

        \(=2^{10}=1024\)

#)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

\(\frac{4^{20}\left(2^{20}+1\right)}{4^{15}+4^{10}+1}=1024\)

Ta có: \(\frac{8^{20}+4^{20}}{4^{25}+64^5}=\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}\) \(=\frac{2^{40}.2^{20}+2^{40}}{2^{30}.2^{20}+2^{30}}=\frac{2^{40}.\left(2^{20}+1\right)}{2^{30}.\left(2^{20}+1\right)}\)\(=\frac{2^{40}}{2^{30}}=2^{10}=1024\)

\(\frac{8^{20}+4^{20}}{4^{25}+64^5}=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}=\frac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}=2^{10}=1024\)

\(\frac{8^{20}+4^{20}}{4^{25}+64^5}=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}=2^{10}=1024\)

\(\frac{8^{20}+4^{20}}{4^{25}+64^5}\)=\(\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}\)=\(\frac{2^{60}+2^{40}}{2^{50}+2^{30}}\)=\(\frac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}\)=\(\frac{2^{40}}{2^{30}}\)= 2¹⁰

1. \(x^{10}=25x^8\Leftrightarrow x^{10}:x^8=25\Leftrightarrow x^2=25=5^2\Leftrightarrow x=5\)

2. \(\frac{8^{20}+4^{20}}{4^{25}+64^5}=\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}=\frac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}=\frac{2^{40}}{2^{30}}=2^{10}\)

1)\(x^{10}=25x^8\)

\(\Rightarrow x^{10}:x^8=25\)

\(\Rightarrow x^2=5^2\)

\(\Rightarrow\orbr{\begin{cases}x=5\\x=-5\end{cases}}\)

2)\(\frac{8^{20}+4^{20}}{4^{25}+64^5}=\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}=\frac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}=2^{10}\)