\[\eqalign{ & a]\;\left[ {{5^3}{{.5}^2}} \right]:5 = [{5^{3 + 2}}]:5 = {5^5}:5 = {5^{5 - 1}} = {5^4} = 625 \cr & b]\;{3^9}:\left[ {{3^3}{{.3}^4}} \right] = {3^9}:{3^{3 + 4}} = {3^9}:{3^7} = {3^{9 - 7}} = {3^2} = 9 \cr & c]\;\left[ {{{13}^6}:{{13}^4}} \right]:{13^2} = {13^{6 - 4}}:{13^2} = {13^2}:{13^2} = 1 \cr & d]\;\left[ {{2^{10}}:{2^7}} \right].\left[ {{2^7}:{2^4}} \right] = {2^{10 - 7}}{.2^{7 - 4}} = {2^3}{.2^3} = {2^{3 + 3}} = {2^6} = 64 \cr} \]
Đề bài
Tính :
a] \[\left[ {{5^3}{{.5}^2}} \right]:5\]
b] \[{3^9}:\left[ {{3^3}{{.3}^4}} \right]\]
c] \[\left[ {{{13}^6}:{{13}^4}} \right]:{13^2}\]
d] \[\left[ {{2^{10}}:{2^7}} \right].\left[ {{2^7}:{2^4}} \right]\].
Lời giải chi tiết
\[\eqalign{ & a]\;\left[ {{5^3}{{.5}^2}} \right]:5 = [{5^{3 + 2}}]:5 = {5^5}:5 = {5^{5 - 1}} = {5^4} = 625 \cr & b]\;{3^9}:\left[ {{3^3}{{.3}^4}} \right] = {3^9}:{3^{3 + 4}} = {3^9}:{3^7} = {3^{9 - 7}} = {3^2} = 9 \cr & c]\;\left[ {{{13}^6}:{{13}^4}} \right]:{13^2} = {13^{6 - 4}}:{13^2} = {13^2}:{13^2} = 1 \cr & d]\;\left[ {{2^{10}}:{2^7}} \right].\left[ {{2^7}:{2^4}} \right] = {2^{10 - 7}}{.2^{7 - 4}} = {2^3}{.2^3} = {2^{3 + 3}} = {2^6} = 64 \cr} \]