Question

Rút gọn

f) \(\frac{25^2.20^4}{5^{10}.4^5}\)

g) \(\frac{16^{12}.8}{32^5.64^4}\)

h) \(\frac{2^{18}.9^4}{6^6.8^4}\)

Answer 1

f) \(\frac{25^2.20^4}{5^{10}.4^5}=\frac{\left(5^2\right)^2.\left(4.5\right)^4}{5^{10}.4^5}=\frac{5^4.5^4.4^4}{5^{10}.4^5}=\frac{5^8.4^4}{5^{10}.4^5}=\frac{1}{5^2.4}=\frac{1}{100}\)

g) \(\frac{16^{12}.8}{32^5.64^4}=\frac{\left(2^4\right)^{12}.2^3}{\left(2^5\right)^5.\left(2^6\right)^4}=\frac{2^{48}.2^3}{2^{25}.2^{24}}=\frac{2^{51}}{2^{49}}=2^2=4\)

h) \(\frac{2^{18}.9^4}{6^6.8^4}=\frac{2^{18}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^4}=\frac{2^{18}.3^8}{2^6.3^6.2^{12}}=\frac{2^{18}.3^8}{2^{18}.3^6}=3^2=9\)