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a) \(\frac{15}{12}+\frac{5}{13}-\frac{3}{12}-\frac{18}{13}\)
\(=\left(\frac{15}{12}-\frac{3}{12}\right)+\left(\frac{5}{13}-\frac{18}{13}\right)\)
\(=1+\left(-1\right)\)
\(=0\)
b) \(\frac{5^4.20^4}{25^5.4^5}=\frac{\left(20.5\right)^4}{\left(25.4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}\)
c) \(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}=\frac{2^{12}.\left(2^{18}+2^8\right)}{2^{12}.\left(1+2^{10}\right)}=\frac{2^{18}+2^8}{1+2^{10}}=256\)
a) \(\dfrac{15}{12}+\dfrac{5}{13}-\dfrac{3}{12}-\dfrac{18}{13}\)
\(=\left(\dfrac{15}{12}-\dfrac{3}{12}\right)+\left(\dfrac{5}{13}-\dfrac{18}{13}\right)\)
\(=\dfrac{12}{12}+\dfrac{-13}{13}\)
\(=1-1\)
\(=0\)
b) \(\dfrac{5^4\cdot20^4}{25^5\cdot4^5}\)
\(=\dfrac{100^4}{100^5}\)
\(=\dfrac{1}{100}\)
a)\(\frac{2^{15}.3^2}{6^6.8^3.4}=\frac{2^{15}.3^2}{2^6.3^6.2^32^2}=\frac{2^{15}.3^2}{2^{\left(6+3+2\right)}.3^6}=\frac{2^{15}.3^2}{2^{11}.3^6}=\frac{2^{\left(15-11\right)}}{3^{\left(6-2\right)}}=\frac{2^3}{3^4}\) viết dài từng bước cho bạn dẽ hiểu
b)\(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}=\frac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(1+2^{10}\right)}=2^{20-12}=2^8\)có thể đua về cơ số 4 thay cơ 2
\(\dfrac{\text{45^{10^{ }}}.5^{10}}{75^{10}}=\dfrac{9^{10}.5^{10}.5^{10}}{5^{10}.5^{10}.3^{10}}=\dfrac{9^{10}}{3^{10}}=3^{10}\)
\(\dfrac{\left(0,8\right)^5}{\left(0,4\right)^6}=\dfrac{2^5.\left(0,4\right)^5}{\left(0,4\right)^6}=\dfrac{2^5}{0,4}=\dfrac{32}{0,4}=80\)
a) \(A=\frac{2^4.25^4}{10^5.5^5}=\frac{2^4.\left(5^2\right)^4}{\left(2.5\right)^5.5^5}=\frac{2^4.5^8}{2^5.5^{10}}=\frac{1}{2.5^2}=\frac{1}{50}\)
b) \(B=\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)
\(B=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}=\frac{2^{10}.3^8.\left(1-3\right)}{2^{10}.3^8.\left(1+5\right)}=\frac{-2}{6}=\frac{-1}{3}\)
\(A=\frac{2^4.25^4}{10^5.5^5}\)
\(A=\frac{2^4.\left(5^2\right)^4}{\left(2.5\right)^5.5^5}\)
\(A=\frac{2^4.5^8}{2^5.5^5.5^5}\)
\(A=\frac{5^8}{2.5^{10}}\)
\(A=\frac{1}{2.5^2}=\frac{1}{2.25}=\frac{1}{50}\)
\(B=\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)
\(B=\frac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(2.3\right)^8.2^2.5}\)
\(B=\frac{2^{10}.3^8-2^{10}.2.3^9}{2^{10}.3^8+2^{10}.3^8.5}\)
\(B=\frac{2^{10}.\left(3^8-2.3^9\right)}{2^{10}.\left(3^8+3^8.5\right)}\)
\(\Rightarrow B=\frac{3^8.2.3^9}{3^8+3^8.5}\) ( \(2^{10}\ne0\))
\(B=\frac{3^8.\left(1-2.3\right)}{3^8.\left(1+5\right)}\)
\(B=\frac{1-6}{1+5}\left(3^8\ne0\right)\)
\(B=\frac{-5}{6}\)
Tham khảo nhé~
\(a,\) \(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=\frac{2^{12}.3^{10}+\left(2.3\right)^9.2^3.3.5}{2^{12}.3^{12}-\left(2.3\right)^{11}}\)
\(=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{\left(2^{12}.3^{10}\right)\left(1+5\right)}{\left(2^{11}.3^{11}\right)\left(2.3-1\right)}\)
\(=\frac{\left(2^{12}.3^{10}\right).6}{\left(2^{11}.3^{11}\right).5}\)
\(=\frac{2.6}{3.5}\)
\(=\frac{2.2}{5}\)
\(=\frac{4}{5}\)
\(b,\) \(\frac{2^{15}.9^4}{6^3.8^3}\)
\(=\frac{2^{15}.3^8}{2^3.3^3.2^9}\)
\(=\frac{2^{15}.3^8}{2^{12}.3^3}\)
\(=2^3.3^5\)
\(=8.243\)
\(=1944\)
Chúc bạn học tốt ^^
a) \(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{\left(2^2\right)^6.\left(3^2\right)^5+6^9.120}{\left(2^3\right)^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}+6^9.120}{2^{12}.3^{12}-6^{11}}=\frac{6^{10}.4+6^{10}.20}{6^{12}-6^{11}}=\frac{6^{10}.\left(4+20\right)}{6^{11}.\left(6-1\right)}=\frac{6^{11}.4}{6^{11}.5}=\frac{4}{5}\)
b) \(\frac{2^{15}.9^4}{6^3.8^3}=\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^3.\left(2^3\right)^3}=\frac{2^{15}.3^8}{2^3.3^3.2^9}=\frac{2^{15}.3^8}{2^{12}.3^3}=2^3.3^5=1944\)
c) \(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{\left(4.2\right)^{10}+4^{10}}{\left(2^3\right)^4+4^6.4^5}=\frac{4^{10}.2^{10}+4^{10}}{2^{12}+4^6.4^5}=\frac{4^{10}.\left(2^{10}+1\right)}{4^6+4^6.2^{10}}=\frac{4^{10}.\left(2^{10}+1\right)}{4^6.\left(1+2^{10}\right)}=\frac{4^{10}}{4^6}=4^4=256\)
a) \(\dfrac{2^{15}.9^4}{6^6.8^3}=\dfrac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}=\dfrac{2^{15}.3^8}{3^6.2^6.2^9}=\dfrac{2^{15}.3^8}{3^6.2^{15}}=3^2=9\)
b) \(\dfrac{45^{15}.5^{15}}{75^{15}}=\dfrac{\left(9.5\right)^{15}.5^{15}}{\left(3.25\right)^{15}}=\dfrac{9^{15}.5^{15}.5^{15}}{3^{15}.25^{15}}=\dfrac{\left(3^2\right)^{15}.5^{30}}{3^{15}.\left(5^2\right)^{15}}\)
\(\dfrac{3^{30}.5^{30}}{3^{15}.5^{30}}=3^{15}=14348907\)
c) \(\dfrac{8^{10}+4^{10}}{8^4+4^{11}}=\dfrac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\dfrac{2^{30}+2^{20}}{2^{12}+2^{22}}=\dfrac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(1+2^{10}\right)}\)
\(=\dfrac{2^{20}}{2^{12}}=2^8=256\)
d) \(\dfrac{ \left(x^2\right)^5}{\left(x^5\right)^2}=\dfrac{x^{10}}{x^{10}}=1\)
Giải:
\(M=\dfrac{8^{10}+4^{10}}{8^4+4^{11}}\)
\(\Leftrightarrow M=\dfrac{2^{10}.4^{10}+4^{10}}{2^4.4^4+4^{11}}\)
\(\Leftrightarrow M=\dfrac{4^{10}\left(2^{10}+1\right)}{4^4.2^4\left(2^{10}+1\right)}\)
\(\Leftrightarrow M=\dfrac{4^6}{2^4}\)
\(\Leftrightarrow M=\dfrac{2^{12}}{2^4}\)
\(\Leftrightarrow M=2^8=256\)
Vậy ...
\(\dfrac{8^{10}+4^{10}}{8^4+4^{11}}=\dfrac{8^4.4^{10}\left(8^6+1\right)}{8^4.4^{10}\left(1+4\right)}=\dfrac{8^6+1}{1+4}=52429\)