Question

sa se compare -3 la puterea 142 și -2 la puterea 213​

Answer 1

$- 3 {}^{142} = - 3 {}^{2 \times 71} = - ({3}^{2} ) {}^{71} = - 9 {}^{71}$

$- 2 {}^{213} = - 2 {}^{3 \times 71} = - (2 {}^{3} ) {}^{71} = - 8 {}^{71}$

$- 9 {}^{71} < - 8 {}^{71} \rightarrow - 3 {}^{142} < - 2 {}^{213}$

Answer 2

Explicație pas cu pas:

$- {3}^{142} = - {3}^{2 \cdot 71} = - {( {3}^{2} )}^{71} = - {9}^{71}$

$- {2}^{213} = - {2}^{3 \cdot 71} = - {( {2}^{3} )}^{71} = - {8}^{71}$

$- 9 < - 8 \iff - {9}^{71} < - {8}^{71} \\ \implies - {3}^{142} < - {2}^{213}$