Question

Aratati ca 3 la puterea 29 - 3 la puterea 27 este cub perfect.

Answer 1

3²⁹ - 3²⁷ =
= 3²⁷(3²-1) =
= 3²⁷*(9-1) =
= 3²⁷*8 =
= 3²⁷*2³ (este cub perfect).

Answer 2

$3^{29}-3^{27} = 3^{27}(3^2-1)=3^{27} (9-1) = 3^{27} \times 8 = (3^9)^3 \times 2^3 =\boxed{((3^9)\times 2)^3}$