Câu 43: So sánh: \({2^{225}};{3^{150}}\)
\({2^{225}} = {2^{3.75}} = {\left( {{2^3}} \right)^{75}} = {8^{75}}\)
\({3^{150}} = {3^{2.75}} = {\left( {{3^2}} \right)^{75}} = {9^{75}}\)
\(8 < 9 \Rightarrow {8^{75}} < {9^{75}}\)
Vậy \({2^{225}} < {3^{150}}\)
Câu 44: Tính:
\(a{)25^3}:{5^2};\)
\(b){\left( {{3 \over 7}} \right)^{21}}:{\left( {{9 \over {49}}} \right)^6};\)
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\(c)3 – {\left( { – {6 \over 7}} \right)^0} + {\left( {{1 \over 2}} \right)^2}:2\)
\(a{)25^3}:{5^2} = {25^3}:25 = {25^2} = 625\)
\(b){\left( {{3 \over 7}} \right)^{21}}:{\left( {{9 \over {49}}} \right)^6} = {\left( {{3 \over 7}} \right)^{21}}:{\left[ {{{\left( {{3 \over 7}} \right)}^2}} \right]^6} \)
\(= {\left( {{3 \over 7}} \right)^{21}}:{\left( {{3 \over 7}} \right)^{12}} = {\left( {{3 \over 7}} \right)^9} = {{19683} \over {40353607}}\)
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\(c) 3 – {\left( { – {6 \over 7}} \right)^0} + {\left( {{1 \over 2}} \right)^2}:2 = 3 – 1 + {\left( {{1 \over 2}} \right)^2}\)
\(= 2 + {1 \over 8} = 2{1 \over 8}\)
Câu 45: Viết các biểu thức số sau dưới dạng \({{\rm{a}}^n}(a \in Q,n \in N)\):
a) \({9.3^3}.{1 \over {81}}{.3^2}\) b) \({4.2^5}:\left( {{2^3}.{1 \over {16}}} \right)\)
c) \({3^2}{.2^5}.{\left( {{2 \over 3}} \right)^2}\) d) \({\left( {{1 \over 3}} \right)^2}.{1 \over 3}{.9^2}\)
a) \({9.3^3}.{1 \over {81}}{.3^2} = \left( {{3^2}{{.3}^3}{{.3}^2}} \right).{1 \over {{3^4}}} = {{{3^7}} \over {{3^4}}} = {3^3}\)
b) \({4.2^5}:\left( {{2^3}.{1 \over {16}}} \right) = {2^2}{.2^5}:\left( {{2^3}.{1 \over {{2^4}}}} \right) \)
\(= {2^7}:{1 \over 2} = {2^7}.2 = {2^8}\)
c) \({3^2}{.2^5}.{\left( {{2 \over 3}} \right)^2} = {3^2}{.2^5}.{{{2^2}} \over {{3^2}}} \)
\(= \left( {{3^2}.{1 \over {{3^2}}}} \right).\left( {{2^5}{{.2}^2}} \right) = {1.2^7} = {2^7}\)
d) \({\left( {{1 \over 3}} \right)^2}.{1 \over 3}{.9^2} = \left( {{1 \over {{3^2}}}.{1 \over 3}} \right).{\left( {{3^2}} \right)^2} = {1 \over {{3^3}}}{.3^4} = 3\)
