Bài 3:
a: \(\frac{45^{10}\cdot5^{10}}{75^{10}}=\left(\frac{45\cdot5}{75}\right)^{10}=\left(\frac{225}{75}\right)^{10}=3^{10}\)
b: \(\frac{2^{17}\cdot9^4}{6^3\cdot8^3}=\frac{2^{17}\cdot3^8}{3^3\cdot2^3\cdot\left(2^3\right)^3}=\frac{2^{17}}{2^3\cdot2^9}\cdot3^5=2^5\cdot3^5=\left(2\cdot3\right)^5=6^5\)
c: \(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}=\frac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(2^{10}+1\right)}=\frac{2^{20}}{2^{12}}=2^8=256\)
Bài 4:
a: \(\frac{7}{12}\cdot3\frac25-\frac{7}{12}\cdot9\frac25\)
\(=\frac{7}{12}\left(3+\frac25-9-\frac25\right)\)
\(=\frac{7}{12}\cdot\left(-6\right)=-\frac72\)
b: \(2\frac{6}{31}-\frac{5}{24}+\frac{25}{31}-1\frac{1}{24}+0,25\)
\(=\left(2+\frac{6}{31}+\frac{25}{31}\right)-\left(\frac{5}{24}+1+\frac{1}{24}\right)+0,25\)
\(=2+1-\left(1+\frac14\right)+\frac14=3-1-\frac14+\frac14=3-1=2\)
c: \(1\frac{8}{15}:\left(-\frac35\right)-5\frac{11}{15}:\left(-\frac35\right)\)
\(=\frac{23}{15}\cdot\frac{-5}{3}-\frac{76}{15}\cdot\frac{-5}{3}\)
\(=-\frac53\left(\frac{23}{15}+\frac{76}{15}\right)=-\frac53\cdot\frac{99}{15}=-\frac53\cdot\frac{33}{5}=-\frac{33}{3}=-11\)
