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\(24^4\cdot3^4-32^{12}:16^{12}\)
\(=72^4-16^{12}\cdot2^{12}:16^{12}\)
\(=72^4-2^{12}\)
\(=26873856-4096\)
\(=26869760\)
a) \(4^8\cdot4^4=\left(2^2\right)^8\cdot\left(2^2\right)^4=2^{16}\cdot2^8=2^{16+8}=2^{24}\)
b) \(5^{12}\cdot7-5^{11}\cdot10\)
\(=5^{11}\cdot\left(5\cdot7-10\right)=5^{11}\cdot\left(35-10\right)=5^{11}\cdot25\)
\(=5^{11}\cdot5^2=5^{11+2}=5^{13}\)
d) \(27^{16}:9^{10}\)
\(=\left(3^3\right)^{16}:\left(3^2\right)^{10}=3^{48}:3^{20}=3^{48-20}=3^{28}\)
e) \(125^3:25^4=\left(5^3\right)^3:\left(5^2\right)^4=5^9:5^8=5^{9-8}=5\)
f) \(24^4:3^4-32^{12}:16^{12}\)
\(=\left(24:4\right)^4-\left(32:16\right)^{12}\)
\(=6^4-2^{12}\)
\(=2^4\cdot\left(3^4-2^8\right)=2^4\cdot-175=-2800\)
D = 244 : 34 - 3212 : 1612
D = (24 : 3)4 - (32 : 16)12
D = 84 - 212
D = (23)4 - 212
D = 212 - 212
D = 0
\(24^4:3^4-32^{12}:16^{12}\)\(=\left(24:3\right)^4-\left(32:16\right)^{12}=8^4-2^{12}=2^{12}-2^{12}=0\)