\(81^3\cdot\frac{1}{9^2}:3^3\)

\(=\left(9^2\right)^3\cdot\frac{1}{9^2}:3^3\)

\(=9^6\cdot\frac{1}{9^2}:3^3\)

\(=9^4:3^3\)

\(=3^8:3^3=3^5\)

=(3^4)3/(3^2)2:3^3

=3^12/3^4:3^3

=3^5

\(81^3\cdot\frac{1}{9^2}:3^3=\left(9^2\right)^3\cdot\frac{1}{9^2}\cdot\frac{1}{3^3}=9^6\cdot\frac{1}{9^2}\cdot\frac{1}{3^3}=\frac{9^6\cdot1\cdot1}{\left(3^2\right)^2\cdot3^3}=\frac{\left(3^2\right)^6}{3^4\cdot3^3}=\frac{3^{12}}{3^7}=3^5\)

a) \({\left( {\frac{8}{9}} \right)^3} \cdot \frac{4}{3} \cdot \frac{2}{3} = {\left( {\frac{8}{9}} \right)^3}.\frac{8}{9} = {\left( {\frac{8}{9}} \right)^{3+1}}={\left( {\frac{8}{9}} \right)^4}\)

b) \({\left( {\frac{1}{4}} \right)^7} \cdot 0,25 = {\left( {0,25} \right)^7}.0,25 ={\left( {0,25} \right)^{7+1}}= {\left( {0,25} \right)^8}\)

c) \({( - 0,125)^6}:\frac{{ - 1}}{8} = {\left( {\frac{{ - 1}}{8}} \right)^6}:\frac{{ - 1}}{8} = {\left( {\frac{{ - 1}}{8}} \right)^{6-1}}= {\left( {\frac{{ - 1}}{8}} \right)^5}\)

d) \({\left[ {{{\left( {\frac{{ - 3}}{2}} \right)}^3}} \right]^2} = {\left( {\frac{{ - 3}}{2}} \right)^{3.2}} = {\left( {\frac{{ - 3}}{2}} \right)^6}\)

\(a,81^3\cdot\frac{1}{9^2}:3^3=\left(9^2\right)^3\cdot\frac{1}{9^2}:3^3=9^6\cdot\frac{1}{9^2}\cdot\frac{1}{3^3}=\frac{9^6}{9^2}\cdot\frac{1}{3^3}=9^4\cdot\frac{1}{3^3}=\left(3^2\right)^4\cdot\frac{1}{3^3}=\frac{3^8}{3^3}=3^5\)

\(b,625^4:25^2=\left(5^4\right)^4:\left(5^2\right)^2=5^{16}:5^4=5^{12}\)

\(3^2\times\frac{1}{243}\times81^2\times\frac{1}{3^3}\)

\(=3^2\times\frac{1}{3^5}\times\left(3^4\right)^2\times\frac{1}{3^3}\)

\(=\left(3^2\times3^8\right)\times\left(\frac{1}{3^5}\times\frac{1}{3^3}\right)\)

\(=3^{10}\times\frac{1}{3^8}\)

\(=3^2\)

\(=9\)

\(\left(4\times2^5\right)\div\left(2^3\times\frac{1}{6}\right)\)

\(=\left(2^2\times2^5\right)\div\left(2^3\times\frac{1}{2\times3}\right)\)

\(=2^7\div2^2\times3\)

\(=2^5\times3\)

\(=96\)

\(3^2.\frac{1}{243}.81^2.\frac{1}{3^3}\)

\(=3^2.\frac{1}{3^5}.\left(3^4\right)^2.\frac{1}{3^3}\)

\(=\left(3^2.3^8\right).\left(\frac{1}{3^5}.\frac{1}{3^3}\right)\)

\(=3^{10}.3^{-8}\)

\(=3^2=9\)

\(\left(4.2^5\right):\left(2^3.\frac{1}{6}\right)\)

\(=2^7:2^2.3\)

\(=2^5.3\)

\(=96\)

ta có : \(3^2.\frac{1}{243}.81^2.\frac{1}{3^2}=\frac{3^2.\left(3^4\right)^2}{3^5.3^2}=\frac{3^2.3^8}{3^5.3^1}=3^3\)

Ta có: \(3^2.\frac{1}{243}.81^2.\frac{1}{3^2}\)

\(=3^2.\frac{1}{3^5}.\left(3^4\right)^2.\frac{1}{3^2}\)

\(=\left(3^2.\frac{1}{3^2}\right).\frac{1}{3^5}.3^8\)

\(=1.\frac{3^8}{3^5}\)

\(=3^3\)

Chuk pạn hok tốt!

3² .1/243.81² .1/3² =27=3³

Chúc bạn học tốt

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

243 : 3⁴ = 3⁵ : 3⁴ = 3^{5 - 4} = 3¹

3^1

\(243:3^4=3^5:3^4=3\)