Вправи: 20.29

20.29 Спростіть вираз (n – ціле число):

1) 25n52n-3 = (52)n52n-3 = 5^{2n–(2n–3)} = 5³ = 125;

2) 12n22n-1 • 3n+1 = (22)n • 3n22n-1 • 3n+1 = 2^{2n–(2n–1)} • 3^n–(n+1) = 2¹ • 3^–1 = 2 • 13 = 23;

3) a4nb2n-1a2nb3+2n = a^4n–2nb^{2n – 1 – (3 + 2n)} = a²ⁿb^–4 = a2nb4.