a: \(\dfrac{2^4\cdot5^2\cdot11^2\cdot7}{2^3\cdot5^3\cdot7^2\cdot11}=\dfrac{2^4}{2^3}\cdot\dfrac{5^2}{5^3}\cdot\dfrac{11^2}{11}\cdot\dfrac{7}{7^2}\)
\(=\dfrac{2}{5}\cdot\dfrac{11}{7}=\dfrac{22}{35}\)
b: \(\dfrac{2^{30}\cdot5^8+2^{13}\cdot5^7}{2^{27}\cdot5^7+2^{10}\cdot5^{27}}\)
\(=\dfrac{2^{13}\cdot5^7\left(2^{17}\cdot5+1\right)}{2^{10}\cdot5^7\left(2^{17}+5^{20}\right)}=\dfrac{2^3\cdot\left(2^{17}\cdot5+1\right)}{2^{17}+5^{20}}\)
c: \(\dfrac{72^3\cdot54^2}{108^4}=\dfrac{\left(2^3\cdot3^2\right)^3\cdot\left(2\cdot3^3\right)^2}{\left(2^2\cdot3^3\right)^4}\)
\(=\dfrac{2^9\cdot3^6\cdot2^2\cdot3^6}{2^8\cdot3^{12}}=\dfrac{2^{11}\cdot3^{12}}{2^8\cdot3^{12}}=2^3=8\)
d: \(\dfrac{2^{10}\cdot3^{10}-2^{10}\cdot3^9}{2^9\cdot3^{10}}=\dfrac{2^{10}\cdot3^9\left(3-1\right)}{2^9\cdot3^{10}}=\dfrac{2}{3}\cdot2=\dfrac{4}{3}\)
