ta có: \(\frac{4^{15}}{7^{30}}=\frac{\left(2^2\right)^{15}}{7^{30}}=\frac{2^{30}}{7^{30}}\)

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

vì\(\frac{2^{30}}{7^{30}}< \frac{3^{30}}{7^{30}}\)nên\(\frac{4^{15}}{7^{30}}< \frac{8^{10}.3^{30}}{7^{30}.4^{15}}\)

CHÚC BẠN HOK TỐT!!!

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\(\frac{4^{15}}{7^{30}}=\frac{2^{30}}{7^{30}}\)  và \(\frac{8^{10}.3^{30}}{7^{30}.4^{15}}=\frac{2^{30}.3^{30}}{7^{30}.2^{30}}=\frac{2^{30}}{7^{30}}\)Vậy hai vế bằng nhau 

Ta có:

\(\frac{4^{15}}{7^{30}}=\frac{\left(2^2\right)^{15}}{7^{30}}=\frac{2^{30}}{7^{30}}=\left(\frac{2}{7}\right)^{30}\)

\(\frac{8^{10}x3^{30}}{7^{30}x4^{15}}=\frac{\left(2^3\right)^{10}x3^{30}}{7^{30}x\left(2^2\right)^{15}}=\frac{2^{30}x3^{30}}{7^{30}x2^{30}}=\frac{3^{30}}{7^{30}}=\left(\frac{3}{7}\right)^{30}\)

Nhận thấy, 2 số đều có cùng số mũ mà \(\frac{3}{7}>\frac{2}{7}\)

=> \(\frac{8^{10}x3^{30}}{7^{30}x4^{15}}>\frac{4^{15}}{7^{30}}\)

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

\(\frac{8^{10}.3^{30}}{7^{30}.1^{15}}=\frac{\left(2^3\right)^{10}.3^{30}}{7^{30}}=\frac{2^{30}.3^{30}}{7^{30}}=\frac{\left(2.3\right)^{30}}{7^{30}}=\frac{6^{30}}{7^{30}}\)

Mà : \(\frac{2^{30}}{7^{10}}=\frac{\left(2^3\right)^{10}}{7^{10}}=\frac{8^{10}}{7^{10}}\)

\(\frac{6^{30}}{7^{30}}=\frac{\left(6^3\right)^{10}}{\left(7^3\right)^{10}}=\frac{216^{10}}{343^{10}}\)

Vì : \(\frac{8}{7}>\frac{216}{343}\Rightarrow\frac{8^{10}}{7^{10}}>\frac{216^{10}}{343^{10}}\)

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

giúp mình vs 

cho n là số tự nhiên

a,   (n+ 10) (n+ 15) chia hết cho 2

b,    n (n+ 1) (n+2) chia hết cho 2 và 3

c,     n (n+ 1) (2n+1) chia hết cho 2 và 3