tính hợp lý \(\dfrac{3^{^{^{ }}6}.45^5-15^{13}:5^9}{27^4.25^3+45^6}\)
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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:
a) \(\dfrac{3^6.45^4-15^{13}.5^{\cdot-9}}{27^4.25^3+45^6}\)
b) \(\dfrac{\left(\dfrac{2}{5}\right)^7.5^7+\left(\dfrac{9}{4}\right)^3:\left(\dfrac{3}{16}\right)^3}{2^7.5^2+512}\)
\(a,=\dfrac{3^6\cdot5^4\cdot9^4-5^{13}\cdot3^{13}\cdot5^{-9}}{3^{12}\cdot5^6+9^6\cdot5^6}=\dfrac{3^{14}\cdot5^4-5^4\cdot3^{13}}{3^{12}\cdot5^6+3^{12}\cdot5^6}\\ =\dfrac{3^{13}\cdot5^4\cdot2}{2\cdot3^{12}\cdot5^6}=\dfrac{3}{5^2}=\dfrac{3}{25}\)
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\(b,=\dfrac{\left(\dfrac{2}{5}\cdot5\right)^7+\left(\dfrac{9}{4}\cdot\dfrac{16}{3}\right)^3}{2^7\cdot5^2+2^9}=\dfrac{2^7+12^3}{2^7\left(5^2+2^2\right)}=\dfrac{2^7+4^3\cdot3^3}{2^7\cdot29}=\dfrac{2^6\left(2+3^3\right)}{2^7\cdot29}=\dfrac{1}{2}\)
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a) \(\dfrac{3^6\cdot3^8\cdot5^4-5^{13}\cdot3^{13}\cdot5^{-9}}{3^{12}\cdot5^6+3^{12}\cdot5^6}=\dfrac{3^{14}\cdot5^4-3^{13}\cdot5^4}{3^{12}\cdot5^6\cdot2}=\dfrac{3^{12}\cdot5^4\left(3^2-3\right)}{3^{12}\cdot5^6\cdot2}=\dfrac{3^2-3}{5^2\cdot2}=\dfrac{6}{50}=\dfrac{3}{25}\)
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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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Tính:\(\frac{3^6.45^4.-15^{13}.5^{-9}}{27^4.25^3+45^6}\)
tính nhanh
\(\frac{3^6.45^4-15^{13}:5^9}{27^4.25^3+45^6}\)
\(\frac{3^6.45^4-15^{13}:5^9}{27^4.25^3+45^6}\)=\(\frac{3^{14}.5^4-3^{13}.5^4}{3^{12}.5^6+3^{12}.5^6}=\frac{3^{13}.5^4\left(3-1\right)}{3^{12}.5^6\left(1+1\right)}\)=\(\frac{3}{25}\)
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