Question

so sánh \(\frac{4^{15}}{7^{30}}\) và \(\frac{8^{10}.3^{10}}{7^{30}.4^{15}}\)

Answer 1

Ta có: \(\frac{4^{15}}{7^{30}}\)=\(\frac{\left(2^2\right)^{15}}{7^{30}}\)=\(\frac{2^{30}}{7^{30}}\)=\(\frac{\left(2^3\right)^{10}}{7^{30}}\)=\(\frac{8^{10}}{7^{30}}\)

\(\frac{8^{10}.3^{10}}{7^{30}.4^{15}}\)=\(\frac{\left(2^3\right)^{10}.3^{10}}{7^{30}.\left(2^2\right)^{15}}\)=\(\frac{2^{30}.3^{10}}{7^{30}.2^{30}}\)=\(\frac{3^{10}}{7^{30}}\)

Vì 8¹⁰>3¹⁰ \(\Rightarrow\)\(\frac{8^{10}}{7^{30}}\)>\(\frac{3^{10}}{7^{30}}\)

Hay \(\frac{4^{15}}{7^{30}}\)>\(\frac{8^{10}.3^{10}}{7^{30}.4^{15}}\)