\(M=\dfrac{3^6.45^4-15^4.9^4}{27^4.25^3+7.45^6}\)
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\(M=\dfrac{3^6.45^4-15^4.9^4}{27^4.25^3+7.45^6}\)
Cho a+b+c=2010 và \(\dfrac{1}{a+b}+\dfrac{1}{a+b}+\dfrac{1}{c+a}=\dfrac{1}{201}TínhS=\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\)
\(M=\dfrac{3^{14}\cdot5^4-3^{12}\cdot5^4}{3^{12}\cdot5^6+7\cdot3^{12}\cdot5^6}=\dfrac{3^{12}\cdot5^4\left(3^2-1\right)}{3^{12}\cdot5^6\left(1+7\right)}=\dfrac{1}{25}\)
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\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)
\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)
\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}=\dfrac{3^6.3^85^4-3^{13}.5^{13}.5^{-9}}{3^{12}.5^6+3^{12}.5^6}\)
\(=\dfrac{3^{14}.5^4-3^{13}.5^4}{2.3^{12}.5^6}=\dfrac{3^{13}.5^4\left(3-1\right)}{2.3^{12}.5^6}\)
\(=\dfrac{3.2}{2.5^2}=\dfrac{3}{25}\)
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\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)?
\(=\dfrac{3^6\cdot\left(3^2\right)^4\cdot5^4-5^{13}\cdot3^{13}\cdot5^{-9}}{3^{12}\cdot5^6+\left(3^2\right)^6\cdot5^6}\)
\(=\dfrac{3^{14}\cdot5^4-5^4\cdot3^{13}}{3^{12}\cdot5^6+3^{12}\cdot5^6}=\dfrac{3^{13}\cdot5^4\cdot2}{2\cdot3^{12}\cdot5^6}=\dfrac{3}{5^2}=\dfrac{3}{25}\)
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\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)
tử số=3^6.45^4-15^13.5^-9=3^6.(5.3^2)^4-(3.5)^13.5^-9=3^6.5^4.3^8-3^13.5^13.5^-9=3^14.5^4-3^13.5^4(3-1)=2.3^13.5^4
mẫu số=27^4.25^3+45^6=3^12.5^6+3^12.5^6=2.3^12.5^6
phân số =(2.3^13.5^4)/2.3^12.5^6=3/25
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\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)
\(=\dfrac{3^{14}\cdot5^4-3^{13}\cdot5^4}{3^{12}\cdot5^6+3^{12}\cdot5^6}\)
\(=\dfrac{3^{13}\cdot5^4\cdot\left(3-1\right)}{2\cdot3^{12}\cdot5^6}=\dfrac{9}{25}\)
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Tính:
\(\dfrac{3^6.45^4-15^3.\dfrac{1}{5^9}}{27^4.25^3+45^6}\)
Tính:
\(\dfrac{3^6.45^4-15^{13}.\dfrac{1}{5^9}}{27^4.25^3+45^6}\)
\(=\dfrac{3^6.\left(3^2.5\right)^4-\left(3.5\right)^{13}.5^{-9}}{\left(3^3\right)^4.\left(5^2\right)^3+\left(3^2.5\right)^6}\)
\(=\dfrac{3^6.3^8.5^4-3^{13}.5^{13}.5^{-9}}{3^{12}.5^6+3^{12}.5^6}\)
\(=\dfrac{3^{14}.5^4-3^{13}.5^4}{3^{12}.5^6+3^{12}.5^6}\)
\(=\dfrac{3^{13}.5^4.\left(3-1\right)}{2.3^{12}.5^6}\)
\(=\dfrac{3.2}{2.5^2}\)
\(=\dfrac{3}{25}.\)
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\(\dfrac{3^6.45^4-15^3.5^{-9}}{27^4.25^3+45^6}\)
\(=\dfrac{3^6.\left(3^2.5\right)^4-\left(5.3\right)^3.5^{-9}}{\left(3^3\right)^4.\left(5^2\right)^3+\left(3^2.5\right)^6}\\ =\dfrac{3^6.3^8.5^4-3^3.5^3.5^{-9}}{3^{12}.5^6+3^{12}.5^6}\\ =\dfrac{3^{14}.5^4-3^3.5^{-6}}{3^{12}.5^6+3^{12}.5^6}\\ =\dfrac{3^3.5^{-6}\left(3^{11}.5^{10}-1\right)}{3^{12}.5^6\left(1+1\right)}\)Hiện mình chỉ làm được đến đây! Để mình suy nghĩ rồi giải tiếp nhé! Chúc bạn học giỏi!!!
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tính nhanh
\(\dfrac{3^6.45^4-15^{13}:5^9}{27^4.25^3+45^6}\)
\(=\dfrac{3^6\cdot3^8\cdot5^4-3^{13}\cdot5^{13}:5^9}{3^{12}\cdot5^6+3^{12}\cdot5^6}\)
\(=\dfrac{3^{14}\cdot5^4-3^{13}\cdot5^4}{3^{12}\cdot5^6\cdot2}=\dfrac{3^{13}\cdot5^4\cdot\left(3-1\right)}{3^{12}\cdot5^6\cdot2}=\dfrac{3}{25}\)
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