rút gọn biểu thức:
\(1,\frac{\left(5^4-5^3\right)^3}{125^4}\)
\(2,\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
các bạn giúp ình với! HELP ME!!!!!!!!!!
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KT
0
L
4
S
5 tháng 1 2023
\(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3-1\right)}\)
\(=\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}.5}\)
\(=\dfrac{2^{12}.3^{10}.6}{2^{11}.3^{11}.5}=\dfrac{2.6}{3.5}=\dfrac{4}{5}\)
XC
0
24 tháng 7 2016
\(=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^4.2^3.7^3}\)
\(=\frac{2^{12}.3^4\left(3-1\right)}{2^{12}.3^5\left(3+1\right)}-\frac{5^{10}.7^3\left(1-7\right)}{5^4.7^3\left(5^5+2^3\right)}\)
\(=\frac{1}{6}+\frac{93750}{3133}\)
1) Ta có: \(\frac{\left(5^4-5^3\right)^3}{125^4}\)
\(=\frac{\left[5^3\cdot\left(5-1\right)\right]^3}{5^{12}}\)
\(=\frac{5^9\cdot4^3}{5^{12}}\)
\(=\frac{4^3}{5^3}=\frac{64}{125}\)
2) Ta có: \(\frac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)
\(=\frac{2^{12}\cdot3^{10}+3^{10}\cdot2^{12}\cdot5}{6^{12}-6^{11}}\)
\(=\frac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{6^{11}\cdot\left(6-1\right)}\)
\(=\frac{6^{11}\cdot2^2}{6^{11}\cdot5}=\frac{2^2}{5}=\frac{4}{5}\)