Câu 50: Tính:
a) \({\rm{}}{\left( {{1 \over 5}} \right)^5}{.5^5}\)
b) \({\left( {0,125} \right)^3}.512\)
c) \({\left( {0.25} \right)^4}.1024\)
a) \({\rm{}}{\left( {{1 \over 5}} \right)^5}{.5^5} = {\left( {{1 \over 5}.5} \right)^5} = {1^5} = 1\)
b) \({\left( {0,125} \right)^3}.512 = {\left( {0,125} \right)^3}{.8^3} = {\left( {0,125.8} \right)^3} = {1^3} = 1\)
c) \({\left( {0,25} \right)^4}.1024 = {\left( {0,25} \right)^4}.256.4 = {\left( {0,25} \right)^4}{.4^4}.4\)
\( = {\left( {0,25.4} \right)^4}.4 = {1^4}.4 = 4\)
Câu 51: Tính:
a) \({{{{120}^3}} \over {{{40}^3}}}\)
b) \({{{{390}^4}} \over {{{130}^4}}}\)
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c) \({{{3^2}} \over {{{\left( {0,375} \right)}^2}}}\)
a) \({{{{120}^3}} \over {{{40}^3}}} = {\left( {{{120} \over {40}}} \right)^3} = {3^3} = 27\)
b) \({{{{390}^4}} \over {{{130}^4}}} = {\left( {{{390} \over {130}}} \right)^4} = {3^4} = 81\)
c) \({{{3^2}} \over {{{\left( {0,375} \right)}^2}}} = {\left( {{3 \over {0,375}}} \right)^2} = {\left( {{{{3 \over 3}} \over 8}} \right)^2} = {8^2} = 64\)
Câu 52: Tính giá trị của các biểu thức sau:
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a) \({\rm{}}{{{{45}^{10}}{{.5}^{20}}} \over {{{75}^{15}}}}\)
b) \({{{{\left( {0,8} \right)}^5}} \over {{{\left( {0,4} \right)}^6}}}\)
c) \({{{2^{15}}{{.9}^4}} \over {{6^6}{{.8}^3}}}\)
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) \({{{2^{15}}{{.9}^4}} \over {{6^6}{{.8}^3}}} = {{{2^{15}}.{{\left( {{3^2}} \right)}^4}} \over {{{\left( {2.3} \right)}^6}.{{\left( {{2^3}} \right)}^3}}} = {{{2^{15}}{{.3}^8}} \over {{2^6}{{.3}^6}{{.2}^9}}} = {3^2} = 9\)
Câu 53
Viết các số sau đây dưới dạng lũy thừa của 3:
1; 243; \({1 \over 3}\); \({1 \over 9}\)
\(1 = {3^0}\);
\(243 = {3^5}\);
\({1 \over 3} = {3^{ – 1}}\);
\({1 \over 9} = {3^{ – 2}}\)
