Bài tập mẫu 4:
\(a.\left[\left(3^{14}\cdot69+3^{14}\cdot12\right):3^{16}-7\right]:2^4\\ =\left[3^{14}\cdot\left(69+12\right):3^{16}-7\right]:2^4\\ =\left(3^{14}\cdot81:3^{16}-7\right):16\\ =\left(3^{14}\cdot3^4:3^{16}-7\right):16\\ =\left(3^{18}:3^{16}-7\right):16\\ =\left(3^2-7\right):16\\ =\left(9-7\right):16\\ =\dfrac{2}{16}=\dfrac{1}{4}\\ b.24^4:3^4-32^{12}:16^{12}\\ =\left(2^3\right)^4\cdot3^4:3^4-\left(2^5\right)^{12}:\left(2^4\right)^{12}\\ =2^{12}-2^{60}:2^{48}\\ =2^{12}-2^{60-48}\\ =2^{12}-2^{12}\\ =0\)
Bài 3:
a: \(\left(10^2+11^2+12^2\right):\left(13^2+14^2\right)\)
\(=\dfrac{100+121+144}{169+196}=\dfrac{365}{365}=1\)
b: \(\dfrac{\left(2^3\cdot9^4+9^3\cdot45\right)}{9^2\cdot10-9^2}\)
\(=\dfrac{2^3\cdot9^4+9^4\cdot5}{9^2\left(10-1\right)}=\dfrac{9^4\cdot\left(2^3+5\right)}{9^3}=9\cdot\left(8+5\right)\)
\(=9\cdot17=153\)
bài 4:
a: \(\dfrac{\left(3^{14}\cdot69+3^{14}\cdot12\right):3^{16}-7}{2^4}\)
\(=\dfrac{3^{14}\cdot\left(69+12\right):3^{16}-7}{16}\)
\(=\dfrac{81:3^2-7}{16}=\dfrac{9-7}{16}=\dfrac{2}{16}=\dfrac{1}{8}\)
b: \(24^4:3^4-32^{12}:16^{12}\)
\(=8^4-2^{12}\)
\(=2^{12}-2^{12}=0\)