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a) \(\frac{4^2.4^3}{2^{10}}\)\
\(=\frac{4^5}{\left(2^2\right)^{10}}=\frac{4^5}{4^{10}}=\frac{1}{4^5}\)
b) \(\frac{0,6^5}{0,2^6}=\frac{\left(0,2.3\right)^5}{0,2^6}=\frac{0,2^5.3^5}{0,2^6}=\frac{3^5}{0,2}=5.3^5\)
\(\frac{3^{17}\cdot81^{11}}{27^{10}\cdot9^{15}}\)
\(=\frac{3^{17}\cdot\left(3^4\right)^{11}}{\left(3^3\right)^{10}\cdot\left(3^2\right)^{15}}\)
\(=\frac{3^{17}\cdot3^{44}}{3^{30}\cdot3^{30}}\)
\(=\frac{3^{61}}{3^{60}}\)
\(=3\)
\(\frac{9^2\cdot2^{11}}{16^2\cdot6^3}\)
\(=\frac{\left(3^2\right)^2\cdot2^{11}}{\left(2^4\right)^2\cdot\left(2\cdot3\right)^3}\)
\(=\frac{3^4\cdot2^{11}}{2^8\cdot2^3\cdot3^3}\)
\(=\frac{3^4\cdot2^{11}}{2^{11}\cdot3^3}\)
\(=\frac{3^4}{3^3}\)
\(=3\)
bài này không khó. Nhưng đánh máy để giải cho bạn thì thực sự khó
a, Ta có: \(\frac{0,8^5}{0,4^6}=\frac{\left(0,4.2\right)^5}{0,4^6}=\frac{0,4^5.2^5}{0,4^6}\) \(=\frac{2^5}{0,4}=80\)
b, Ta có: \(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}\) \(=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}=\frac{2^{12}\left(2^{18}+2^8\right)}{2^{12}\left(1+2^{10}\right)}\)
\(=\frac{2^{18}+2^8}{1+2^{10}}=\frac{2^8\left(2^{10}+1\right)}{2^{10}+1}=2^8\)
c, Ta có: \(\frac{2^{15}.9^4}{6^3.8^3}=\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^3.\left(2^3\right)^3}=\frac{2^{15}.3^8}{2^3.3^3.2^9}\) \(=\frac{2^{15}.3^8}{2^{12}.3^3}=2^3.3^5=1944\)
b)\(\frac{8^{10}+4^{10}}{8^4+4^{11}}\)=\(\frac{\left(2.4\right)^{10}+4^{10}}{\left(2.4\right)^{10}+4^{11}}\)=\(\frac{2^{10}.4^{10}+4^{10}.1}{2^{10}.4^{10}+4^{10}.4}\)=\(\frac{4^{10}\left(2^{10}+1\right)}{4^{10}\left(2^{10}+4\right)}\)=\(\frac{4^{10}.1025}{4^{10}.1028}\)=\(\frac{1025}{1028}\)
B = \(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.\left(3^2\right)^3}{\left(2.3\right)^5.\left(2^3\right)^2}\)\(=\frac{2^7.3^6}{2^5.3^5.2^6}\)
Đề có chỉ kêu rút gọn thôi phải k nhỉ?