Question

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!!!!!!!!!!

Answer 1

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: \(\frac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)

\(=\frac{2^{12}\cdot3^{10}+3^{10}\cdot2^{12}\cdot5}{6^{12}-6^{11}}\)

\(=\frac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{6^{11}\cdot\left(6-1\right)}\)

\(=\frac{6^{11}\cdot2^2}{6^{11}\cdot5}=\frac{2^2}{5}=\frac{4}{5}\)