Question

Comparati numerele:33 la puterea 3 si 3 la puterea 33.

Answer 1

33³ = (11 x 3)³ = 11³ x 3³
3³³ = 3³⁰⁺³ = 3³⁰ x 3³

comparam acum 11³ si 3³⁰
11³ = 11 x 11 x 11 = 1331
3⁷ =  3 x 3 x 3 x 3 x 3 x 3 x 3 = 2187 ⇒3⁷ > 11³ ⇒ 3³⁰ > 11³
⇒ 3³³ > 33³

Answer 2

$\it \dfrac{3^{33}}{33^3} = \dfrac{3\cdot3\cdot3\cdot3^{30}}{33\cdot33\cdot33} = \dfrac{(3^{10})^3}{11^3} = \left(\dfrac{3^{10}}{11}\right)^3 \ \textgreater \ 1, deoarece\ 3^{10}\ \textgreater \ 11$

$\it Deci\ \ \dfrac{3^{33}}{33^3} \ \textgreater \ 1 \Longrightarrow 3^{33} \ \textgreater \ 33^3.$