Question

[dothithuuyen]

Bài 1: Tính giá trị biểu thức:

      a, \(\frac{5^5.20^3-5^4.20^3+5^7.4^5}{\left(20+5\right)^3.4^5}\)

     b, \(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)

     c, \(\frac{5.\left(3.7^{15}-19.7^{14}\right)}{7^{16}+3.7^{15}}\)

Answer 1

[Edogawa Conan]

a) \(\frac{5^5.20^3-5^4.20^3+5^7.4^5}{\left(20+5\right)^3.4^5}\)

= \(\frac{5^5.\left(2^2.5\right)^3-5^4.\left(2^2.5\right)^3+5^7.\left(2^2\right)^5}{\left(5^2\right)^3.\left(2^2\right)^5}\)

= \(\frac{5^5.2^6.5^3-5^4.2^6.5^3+5^7.2^{10}}{5^6.2^{10}}\)

= \(\frac{5^8.2^6-5^7.2^6+5^7.2^{10}}{5^6.2^{10}}\)

= \(\frac{5^7.2^6.\left(5-1+2^4\right)}{5^6.2^{10}}\)

= \(\frac{5.20}{2^4}=\frac{25}{4}\)

Answer 2

[zZz Cool Kid_new zZz]

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

\(=\frac{2^{12}\cdot3^{10}+2^3\cdot3\cdot5\cdot2^9\cdot3^9}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)

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

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

\(=\frac{2^{13}\cdot3^{11}}{2^{11}\cdot3^{11}\cdot5}=\frac{2^2}{5}=\frac{4}{5}\)