a) \(\displaystyle {{{{45}^{10}}{{.5}^{20}}} \over {{{75}^{15}}}} = {{{{\left( {3.15} \right)}^{10}}{{.5}^{20}}} \over {{{\left( {5.15} \right)}^{15}}}} \)
\(\displaystyle = {{{3^{10}}{{.15}^{10}}{{.5}^{20}}} \over {{5^{15}}{{.15}^{15}}}} = {{{3^{10}}{{.5}^5}} \over {{{15}^5}}}\)
\(\displaystyle = {{{3^{10}}{{.5}^5}} \over {{3^5}{{.5}^5}}} = {3^5} = 243\)
b) \(\displaystyle {{{{\left( {0,8} \right)}^5}} \over {{{\left( {0,4} \right)}^6}}} = {{{{\left( {0,8} \right)}^5}} \over {{{\left( {0,4} \right)}^5}.0,4}}\)
\(\displaystyle = {\left( {{{0,8} \over {0,4}}} \right)^5}.{1 \over {0,4}} = {2^5}.{1 \over {\displaystyle {2 \over 5}}} \)
\(\displaystyle= {2^5}.{5 \over 2} = {2^4}.5 = 16.5 = 80\)
c) \(\displaystyle {{{2^{15}}{{.9}^4}} \over {{6^6}{{.8}^3}}} = {{{2^{15}}.{{\left( {{3^2}} \right)}^4}} \over {{{\left( {2.3} \right)}^6}.{{\left( {{2^3}} \right)}^3}}} \)
\(\displaystyle = {{{2^{15}}{{.3}^8}} \over {{2^6}{{.3}^6}{{.2}^9}}} = {3^2} = 9\)
