Tính giá trị của các biểu thức sau:
a) \({\rm{}}{{{{45}^{10}}{{.5}^{20}}} \over {{{75}^{15}}}}\)
b) \({{{{\left( {0,8} \right)}^5}} \over {{{\left( {0,4} \right)}^6}}}\)
c) \({{{2^{15}}{{.9}^4}} \over {{6^6}{{.8}^3}}}\)
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a) \({\rm{}}{{{{45}^{10}}{{.5}^{20}}} \over {{{75}^{15}}}} = {{{{\left( {3.15} \right)}^{10}}{{.5}^{20}}} \over {{{\left( {5.15} \right)}^{15}}}} = {{{3^{10}}{{.15}^{10}}{{.5}^{20}}} \over {{5^{15}}{{.15}^{15}}}} = {{{3^{10}}{{.5}^5}} \over {{{15}^5}}}\)
\(= {{{3^{10}}{{.5}^5}} \over {{3^5}{{.5}^5}}} = {3^5} = 243\)
b) \({{{{\left( {0,8} \right)}^5}} \over {{{\left( {0,4} \right)}^6}}} = {{{{\left( {0,8} \right)}^5}} \over {{{\left( {0,4} \right)}^5}.0,4}} = {\left( {{{0,8} \over {0,4}}} \right)^5}.{1 \over {0,4}}\)
\(= {2^5}.{1 \over {{2 \over 5}}} = {2^5}.{5 \over 2} = {2^4}.5 = 16.5 = 80\)
c) \({{{2^{15}}{{.9}^4}} \over {{6^6}{{.8}^3}}} = {{{2^{15}}.{{\left( {{3^2}} \right)}^4}} \over {{{\left( {2.3} \right)}^6}.{{\left( {{2^3}} \right)}^3}}} = {{{2^{15}}{{.3}^8}} \over {{2^6}{{.3}^6}{{.2}^9}}} = {3^2} = 9\)