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Thực hiện phép tính.a) $\dfrac{5^{16}.27^7}{125^5.9^{11}}$        b)$\left(0,2\right)^2.5-\dfrac{2^{13}.7^3}{4^6.9^5}$c)$\dfrac{5^6+2^2.25^3+2^3.125^2}{26.5^6}$

Tryechun🥶 · Accepted Answer

$a.\dfrac{5^{16}.27^7}{125^5.9^{11}}=\dfrac{5^{16}.\left(3^3\right)^7}{\left(5^3\right)^5.\left(3^2\right)^{11}}=\dfrac{5^{16}.3^{21}}{5^{15}.3^{22}}=\dfrac{5}{3}\ b.\left(0,2\right)^2.5-\dfrac{2^{13}.7^3}{4^6.9^5}\
=0,04.5-\dfrac{2^{13}.7^3}{\left(2^2\right)^6.\left(3^2\right)^5}\
=0,2-\dfrac{2^{13}.343}{2^{12}.3^{10}}\
=\dfrac{1}{5}-\dfrac{2.343}{59049}\
=\dfrac{1}{5}-\dfrac{686}{59049}\
=0,1883825298$$c.\dfrac{5^6+2^2.25^3+2^3.125^2}{26.5^6}\
=\dfrac{5^6+2^2.\left(5^2\right)^3+2^3.\left(5^3\right)^2}{26.5^6}\
=\dfrac{5^6+2^2.5^6+2^3.5^6}{26.5^6}\
=\dfrac{5^6.\left(1+2^2+2^3\right)}{26.5^6}\
=\dfrac{5^6.13}{26.5^6}=\dfrac{13}{26}=\dfrac{1}{2}$Câu trả lời: $a.\dfrac{5^{16}.27^7}{125^5.9^{11}}=\dfrac{5^{16}.\left(3^3\right)^7}{\left(5^3\right)^5.\left(3^2\right)^{11}}=\dfrac{5^{16}.3^{21}}{5^{15}.3^{22}}=\dfrac{5}{3}\ b.\left(0,2\right)^2.5-\dfrac{2^{13}.7^3}{4^6.9^5}\
=0,04.5-\dfrac{2^{13}.7^3}{\left(2^2\right)^6.\left(3^2\right)^5}\
=0,2-\dfrac{2^{13}.343}{2^{12}.3^{10}}\
=\dfrac{1}{5}-\dfrac{2.343}{59049}\
=\dfrac{1}{5}-\dfrac{686}{59049}\
=0,1883825298$$c.\dfrac{5^6+2^2.25^3+2^3.125^2}{26.5^6}\
=\dfrac{5^6+2^2.\left(5^2\right)^3+2^3.\left(5^3\right)^2}{26.5^6}\
=\dfrac{5^6+2^2.5^6+2^3.5^6}{26.5^6}\
=\dfrac{5^6.\left(1+2^2+2^3\right)}{26.5^6}\
=\dfrac{5^6.13}{26.5^6}=\dfrac{13}{26}=\dfrac{1}{2}$

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