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\(81^3\cdot\frac{1}{9^2}:3^3\)
\(=\left(9^2\right)^3\cdot\frac{1}{9^2}:3^3\)
\(=9^6\cdot\frac{1}{9^2}:3^3\)
\(=9^4:3^3\)
\(=3^8:3^3=3^5\)
\(a,81^3\cdot\frac{1}{9^2}:3^3=\left(9^2\right)^3\cdot\frac{1}{9^2}:3^3=9^6\cdot\frac{1}{9^2}\cdot\frac{1}{3^3}=\frac{9^6}{9^2}\cdot\frac{1}{3^3}=9^4\cdot\frac{1}{3^3}=\left(3^2\right)^4\cdot\frac{1}{3^3}=\frac{3^8}{3^3}=3^5\)
\(b,625^4:25^2=\left(5^4\right)^4:\left(5^2\right)^2=5^{16}:5^4=5^{12}\)
\(3^2\times\frac{1}{243}\times81^2\times\frac{1}{3^3}\)
\(=3^2\times\frac{1}{3^5}\times\left(3^4\right)^2\times\frac{1}{3^3}\)
\(=\left(3^2\times3^8\right)\times\left(\frac{1}{3^5}\times\frac{1}{3^3}\right)\)
\(=3^{10}\times\frac{1}{3^8}\)
\(=3^2\)
\(=9\)
\(\left(4\times2^5\right)\div\left(2^3\times\frac{1}{6}\right)\)
\(=\left(2^2\times2^5\right)\div\left(2^3\times\frac{1}{2\times3}\right)\)
\(=2^7\div2^2\times3\)
\(=2^5\times3\)
\(=96\)
\(3^2.\frac{1}{243}.81^2.\frac{1}{3^3}\)
\(=3^2.\frac{1}{3^5}.\left(3^4\right)^2.\frac{1}{3^3}\)
\(=\left(3^2.3^8\right).\left(\frac{1}{3^5}.\frac{1}{3^3}\right)\)
\(=3^{10}.3^{-8}\)
\(=3^2=9\)
\(\left(4.2^5\right):\left(2^3.\frac{1}{6}\right)\)
\(=2^7:2^2.3\)
\(=2^5.3\)
\(=96\)
a/ (26.16) :42
=(26.22) :(22)2
=28 : 24=24=16
b/ (510:625) : 25
= (510:54) :52
=56 : 52=53=625
c/ (81.243):3
= (34.35) :3
= 39 :3=38 =6561
\(3^2\cdot\frac{1}{243}\cdot81^2\cdot\frac{1}{3^2}=3^2\cdot\frac{1}{3^5}\cdot3^8\cdot\frac{1}{3^2}=3^{10}\cdot\frac{1}{3^7}=3^3\)