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

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A = (30: 7\(\dfrac{1}{2}\)) : (\(\dfrac{1}{15}\):0,5) -1,5\(\times\)(4\(\dfrac{1}{2}\)-\(\dfrac{9}{2}\))

A = (30 : \(\dfrac{15}{2}\)): (\(\dfrac{1}{15}\) \(\times\) 2) - 1,5 \(\times\) (\(\dfrac{9}{2}\) - \(\dfrac{9}{2}\))

A = (30 \(\times\) \(\dfrac{2}{15}\)) : \(\dfrac{2}{15}\) - 1,5 \(\times\) 0

A = 4 \(\times\) \(\dfrac{15}{2}\) - 0

A = 30

\(\frac{4^{15}}{7^{30}}=\frac{2^{30}}{7^{30}}\)  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 \(\frac{3}{7}>\frac{2}{7}\)

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