Đáp án:
a) $25^{15}<8^{10}.3^{30}$
b) $\dfrac{4^{15}}{7^{30}}<\dfrac{8^{10}.3^{30}}{7^{30}.4^{15}}$
Giải thích các bước giải:
a)
Ta có:
$25^{15}=(5^2)^{15}=5^{30}$
$8^{10}.3^{30}=(2^3)^{10}.3^{30}=2^{30}.3^{30}=(2.3)^{30}=6^{30}$
Vì $5<6$ nên $5^{30}<6^{30}$ hay $25^{15}<8^{10}.3^{30}$
Vậy $25^{15}<8^{10}.3^{30}$.
b)
Ta có:
$\dfrac{4^{15}}{7^{30}}=\dfrac{(2^2)^{15}}{7^{30}}=\dfrac{2^{30}}{7^{30}}=\left(\dfrac{2}{7}\right)^{30}$
$\dfrac{8^{10}.3^{30}}{7^{30}.4^{15}}=\dfrac{(2^3)^{10}.3^{30}}{7^{30}.(2^2)^{15}}=\dfrac{2^{30}.3^{30}}{7^{30}.2^{30}}=\dfrac{3^{30}}{7^{30}}=\left(\dfrac{3}{7}\right)^{30}$
Vì $\dfrac{2}{7}<\dfrac{3}{7}$ nên $\left(\dfrac{2}{7}\right)^{30} < \left(\dfrac{3}{7}\right)^{30}$
Vậy $\dfrac{4^{15}}{7^{30}}<\dfrac{8^{10}.3^{30}}{7^{30}.4^{15}}$.
