Đáp án:
$(0,4)^{14}<(0,8)^3$
Giải thích các bước giải:
$(0,4)^{14}=\left(\dfrac25\right)^{\large14}=\left(\dfrac25\right)^{\large12}\cdot\dfrac{4}{25}$
Vì $\dfrac{4}{25}<1$ nên $\left(\dfrac25\right)^{\large12}\cdot\dfrac{4}{25}<\left(\dfrac25\right)^{\large12}$
$\left(\dfrac25\right)^{\large12}=\left(\dfrac25\right)^{\large3.4}=\left(\dfrac{16}{625}\right)^3$
$(0,8)^3=\left(\dfrac45\right)^{\large3}$
$\Rightarrow \dfrac{16}{625}<\dfrac45\Rightarrow \left(\dfrac{16}{625}\right)^{\large3}<\left(\dfrac45\right)^{\large3}$
$\Rightarrow \left(\dfrac25\right)^{\large14}<\left(\dfrac25\right)^{\large12}<\left(\dfrac45\right)^{\large3}$
$\Rightarrow (0,4)^{14}<(0,8)^3$
Vậy $(0,4)^{14}<(0,8)^3$.
