Tính giá trị các biểu thức
a) \(\dfrac{{{9^3}{{.2}^{10}}}}{{{{16}^2}{{.81}^2}}}\)
b) \(\dfrac{{{{( - 3)}^7}.{{( - 3)}^8}}}{{{{7.9}^7}}}\)
c) \(\dfrac{{{{(0,3)}^6}.{{(0,04)}^3}}}{{{{(0,09)}^4}.{{(0,2)}^4}}}\)
d) \(\dfrac{{{2^3} + {2^4} + {2^5} + {2^6}}}{{{{15}^2}}}\)
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\(a)\dfrac{{{9^3}{{.2}^{10}}}}{{{{16}^2}{{.81}^2}}} = \dfrac{{{9^3}{{.2}^{10}}}}{{{{({2^4})}^2}.{{({9^2})}^2}}} = \dfrac{{{9^3}{{.2}^{10}}}}{{{2^8}{{.9}^4}}} = \dfrac{{{2^2}}}{9} = \dfrac{4}{9}\\b)\dfrac{{{{( - 3)}^7}.{{( - 3)}^8}}}{{{{7.9}^7}}} = \dfrac{{{{( - 3)}^{15}}}}{{7.{{\left[ {{{\left( { - 3} \right)}^2}} \right]}^7}}} = \dfrac{{{{( - 3)}^{15}}}}{{7.{{( - 3)}^{14}}}} = \dfrac{{ - 3}}{7}\\c)\dfrac{{{{(0,3)}^6}.{{(0,04)}^3}}}{{{{(0,09)}^4}.{{(0,2)}^4}}} = \dfrac{{{{(0,3)}^6}.{{(0,{2^2})}^3}}}{{{{(0,{3^2})}^4}.{{(0,2)}^4}}}\\ = \dfrac{{{{(0,3)}^6}.{{(0,2)}^6}}}{{{{(0,3)}^8}.{{(0,2)}^4}}} = \dfrac{{{{(0,2)}^2}}}{{{{(0,3)}^2}}} = \dfrac{{0,04}}{{0,09}} = \dfrac{4}{9}\)
d) Cách 1: \(\dfrac{{{2^3} + {2^4} + {2^5} + {2^6}}}{{{{15}^2}}} = \dfrac{{8 + 16 + 32 + 64}}{{225}} = \dfrac{{120}}{{225}} = \dfrac{8}{{15}}\)
Cách 2: \(\dfrac{{{2^3} + {2^4} + {2^5} + {2^6}}}{{{{15}^2}}} = \dfrac{2^3.(1+2+2^2+2^3)}{{15^2}} = \dfrac{{8.15}}{{15^2}} = \dfrac{8}{{15}}\)