Can it happen that for some integer m ≠ 0 (\(\frac{4}{25}\))m = \((

1.	Can it happen that for some integer m ≠ 0 (\(\frac{4}{25}\))m = \((\frac{2}{5})^{m^2}\) ?
Answer» (4/25)^m = (2/5)^{m^2} (2²/5²)^m = (2/5)^m^² (2/5)^2m = (2/5)^{m^2} ∴ m² = 2m m.m = 2m m = 2 It can happen if m = 2

Can it happen that for some integer m ≠ 0 (\(\frac{4}{25}\))m = \((\frac{2}{5})^{m^2}\) ?

Answer»

(4/25)^m = (2/5)^{m^2}

(2²/5²)^m = (2/5)^m^²

(2/5)^2m = (2/5)^{m^2}

∴ m² = 2m

m.m = 2m

m = 2

It can happen if m = 2