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a) 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=3^13.5^4(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
\(\frac{3^6.45^4-15^{13}:5^9}{27^4.25^3+45^6}\)=\(\frac{3^{14}.5^4-3^{13}.5^4}{3^{12}.5^6+3^{12}.5^6}=\frac{3^{13}.5^4\left(3-1\right)}{3^{12}.5^6\left(1+1\right)}\)=\(\frac{3}{25}\)
\(\frac{3^6.3^8.5^4-3^{13}.5^{13}:5^9}{3^{12}.5^6+3^{12}.5^6}=\frac{3^{14}.5^4-3^{13}.5^4}{2.3^{12}.5^6}=\frac{2.3^{13}.5^4}{2.3^{12}.5^6}=\frac{1}{75}\)
\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}=\dfrac{3^6.3^85^4-3^{13}.5^{13}.5^{-9}}{3^{12}.5^6+3^{12}.5^6}\)
\(=\dfrac{3^{14}.5^4-3^{13}.5^4}{2.3^{12}.5^6}=\dfrac{3^{13}.5^4\left(3-1\right)}{2.3^{12}.5^6}\)
\(=\dfrac{3.2}{2.5^2}=\dfrac{3}{25}\)
Ta có : \(A=\frac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3.45^6}\)
=\(\frac{3^6.5^4.3^8-3^{13}.5^{13}.5^{-9}}{3^{12}.5^6+5^6.3^{12}}\)
=\(\frac{3^{14}.5^4-3^{13}.5^4}{3^{12}.5^6+5^6.3^{12}}=\frac{3^{13}.5^4.\left(3-1\right)}{5^6.3^{12}.\left(1+1\right)}=\frac{3}{5^2}=\frac{3}{25}\)
\(\frac{3^6\times45^4-15^{13}\times5^{-9}}{27^4\times25^3+45^6}\)
= \(\frac{3^6\times\left(3^2\right)^6\times5^6-3^{13}\times5^{13}\times5^{-9}}{3^{12}\times5^6+\left(3^2\right)^6\times5^6}\)
= \(\frac{3^6\times3^{12}\times5^6-3^{13}\times5^4}{3^{12}\times5^6\times\left(1+1\right)}\)
= \(\frac{3^{13}\times5^4\times\left(3^5\times5^2-1\right)}{3^{12}\times5^6\times2}\)
= \(\frac{3\times\left(3^5\times5^2-1\right)}{5^2\times2}=\frac{3^6\times3\times5^2-3}{5^2\times2}\)
Bạn dựa vào đáp án của mình rồi giải tiếp nhé. Chúc bạn học tốt!
\(=\frac{3^6.3^8.5^4-3^{13}.5^{13}.\frac{1}{5^9}}{3^{12}.5^6+3^{12}.5^6}\)
\(=\frac{3^{13}.5^4\left(3-1\right)}{3^{12}.5^6.2}\)
\(=\frac{3}{5^2}=\frac{3}{25}\)