Đề bài

Tìm x, biết: a) \(x:{\left( {\frac{{ - 1}}{2}} \right)^3} =  - \frac{1}{2};\) b) \(x.{\left( {\frac{3}{5}} \right)^7} = {\left( {\frac{3}{5}} \right)^9};\) c) \({\left( {\frac{{ - 2}}{3}} \right)^{11}}:x = {\left( {\frac{{ - 2}}{3}} \right)^9};\) d) \(x.{\left( {0,25} \right)^6} = {\left( {\frac{1}{4}} \right)^8}\)

Lời giải chi tiết

a) \(x:{\left( {\frac{{ - 1}}{2}} \right)^3} =  - \frac{1}{2}\) \(\begin{array}{l}x =  - \frac{1}{2}.{\left( {\frac{{ - 1}}{2}} \right)^3}\\x = {\left( {\frac{{ - 1}}{2}} \right)^4}\\x = \frac{1}{{16}}\end{array}\)               Vậy \(x = \frac{1}{{16}}\).  b) \(x.{\left( {\frac{3}{5}} \right)^7} = {\left( {\frac{3}{5}} \right)^9}\) \(\begin{array}{l}x = {\left( {\frac{3}{5}} \right)^9}:{\left( {\frac{3}{5}} \right)^7}\\x = {\left( {\frac{3}{5}} \right)^2}\\x = \frac{9}{{25}}\end{array}\) Vậy \(x = \frac{9}{{25}}\). c) \({\left( {\frac{{ - 2}}{3}} \right)^{11}}:x = {\left( {\frac{{ - 2}}{3}} \right)^9}\) \(\begin{array}{l}x = {\left( {\frac{{ - 2}}{3}} \right)^{11}}:{\left( {\frac{{ - 2}}{3}} \right)^9}\\x = {\left( {\frac{{ - 2}}{3}} \right)^2}\\x = \frac{4}{9}.\end{array}\)          Vậy \(x = \frac{4}{9}\). d) \(x.{\left( {0,25} \right)^6} = {\left( {\frac{1}{4}} \right)^8}\) \(\begin{array}{l}x.{\left( {\frac{1}{4}} \right)^6} = {\left( {\frac{1}{4}} \right)^8}\\x = {\left( {\frac{1}{4}} \right)^8}:{\left( {\frac{1}{4}} \right)^6}\\x = {\left( {\frac{1}{4}} \right)^2}\\x = \frac{1}{{16}}\end{array}\) Vậy \(x = \frac{1}{{16}}\).