Question

3. Tính: M=\(\frac{8^{10}+4^{10}}{8^4+4^{11}}\)

Answer 1

3: Tính

Ta có: \(M=\frac{8^{10}+4^{10}}{8^4+4^{11}}\)

\(=\frac{4^{10}\cdot2^{10}+4^{10}\cdot1}{4^4\cdot2^4+4^4\cdot4^7}\)

\(=\frac{4^{10}\left(2^{10}+1\right)}{4^4\left(2^4+4^7\right)}\)

\(=4^6\cdot\frac{2^{10}+1}{2^4\cdot1+2^4\cdot2^7\cdot2^3}\)

\(=4^6\cdot\frac{2^{10}+1}{2^4\left(1+2^{10}\right)}=\frac{4^6}{2^4}=\frac{2^6\cdot2^6}{2^4}=2^2\cdot2^6\)

\(=2^8=256\)

Vậy: M=256

Answer 2

Ta có: M= \(\frac{8^{10}+4^{10}}{8^4+4^{11}}\)

=> M= \(\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}=\frac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(1+2^{10}\right)}=\frac{2^{20}}{2^{12}}=2^8=256\)

Chúc bạn học tốt!