Tính và so sánh:
\(a)\,\,{\left( {\dfrac{{ – 2}}{3}} \right)^3}\) và \(\dfrac{{{{\left( { – 2} \right)}^3}}}{{{3^3}}}\)
\(b)\,\,\dfrac{{{{10}^5}}}{{{2^5}}}\) và \({\left( {\dfrac{{10}}{2}} \right)^5}\)
\({x^n} = \underbrace {x \ldots x}_{n\;thừa \;số}\)
Nếu \(x = \dfrac{a}{b}\) thì \({x^n} = {\left( {\dfrac{a}{b}} \right)^n} = \dfrac{{{a^n}}}{{{b^n}}}\)
\(\eqalign{
& a)\,\,{\left( {{{ – 2} \over 3}} \right)^3} = {{{{\left( { – 2} \right)}^3}} \over {{3^3}}} = {{ – 8} \over {27}} \cr
& {{{{\left( { – 2} \right)}^3}} \over {{3^3}}} = {{ – 8} \over {27}} \cr
& \Rightarrow \,{\left( {{{ – 2} \over 3}} \right)^3} = {{{{\left( { – 2} \right)}^3}} \over {{3^3}}} \cr
& b)\,\,{{{{10}^5}} \over {{2^5}}} = {{100000} \over {32}} = 3125 \cr
& {\left( {{{10} \over 2}} \right)^5} = {\left( 5 \right)^5} = 3125 \cr
& \Rightarrow {{{{10}^5}} \over {{2^5}}} = {\left( {{{10} \over 2}} \right)^5} \cr} \)