a, \(A=\dfrac{3^{10}.11+3^{10}.5}{3^9.2^4}=\dfrac{3^{10}.\left(11+5\right)}{3^9.2^4}\)
\(=\dfrac{3^{10}.2^4}{3^9.2^4}=3\)
b, \(B=\dfrac{2^{10}.13+2^{10}.65}{2^8.104}=\dfrac{2^{10}.78}{2^8.104}\)
\(=\dfrac{2^2.3}{4}=3\)
c, \(C=\dfrac{4^9.36+64^4}{16^4.100}=\dfrac{\left(2^2\right)^9.36+\left(2^6\right)^4}{\left(2^4\right)^4.100}\)
\(=\dfrac{2^{18}.36+2^{24}}{2^{16}.100}=\dfrac{2^{18}.\left(36+2^6\right)}{2^{16}.100}\)
\(=\dfrac{2^4.100}{100}=2^4=16\)
Câu d làm tương tự! Chúc bạn học tốt!!!
d, \(D=\dfrac{72^3.54^2}{108^4}=\dfrac{\left(2^3.3^2\right)^3.\left(2.3^3\right)^2}{\left(2^2.3^3\right)^4}\)
\(=\dfrac{2^9.3^6.2^2.3^6}{2^8.3^{12}}=2^3=8\)
Chúc bạn học tốt!!!
\(a=\dfrac{3^{10}.11+3^{10}.5}{3^9.2^4}=\dfrac{3^{10}\left(11+5\right)}{3^9.16}=\dfrac{3^{10}.16}{3^9.16}=\dfrac{3^{10}}{3^9}=3\)
\(b=\dfrac{2^{10}.13+2^{10}.65}{2^8.104}=\dfrac{2^{10}\left(13+65\right)}{2^8.2^2.26}=\dfrac{2^{10}.78}{2^{10}.26}=\dfrac{78}{26}=3\)
\(c=\dfrac{4^9.36+64^4}{16^4.100}=\dfrac{4^9.36+\left(4^3\right)^4}{\left(4^2\right)^4.100}=\dfrac{4^9.36+4^{12}}{4^8.100}=\dfrac{4^9.36+4^9.4^3}{4^8.100}=\dfrac{4^9.36+4^9.64}{4^8.100}=\dfrac{4^9\left(36+64\right)}{4^8.100}=\dfrac{4^9.100}{4^8.100}=\dfrac{4^9}{4^8}=4\)
\(d=\dfrac{72^3.54^2}{108^4}=\dfrac{\left(2^3.3^2\right)^3.\left(2.3^3\right)^2}{\left(2^2.3^3\right)^4}=\dfrac{2^9.3^6.2^2.3^6}{2^8.3^{12}}=\dfrac{2^{11}.3^{12}}{2^8.3^{12}}=\dfrac{2^{11}}{2^8}=2^3=8\)