Вправи: 855

855. Скоротіть дріб (n — ціле число):

1) 9n-132n-3 = (32)n-132n-3 = 32n-232n-3 = 3^{(2n–2)–(2n–3)} = 3^{2n–2–2n+3} = 3¹ = 3;

2) 7n+1 • 2n-114n = 7n • 7 • 2n • 2-12n • 7n = 7 • 2^–1 = 7 • 12 = 3,5;

3) 22n-1 • 3n+112n = 22n • 2-1 • 3n • 3(4 • 3)n = 22n • 2-1 • 3n • 322n • 3n = 12 • 3 = 1,5;

4) a6+ a11a-4+ a = a6(1+ a5)a-4(1+ a5) = a6a-4 = a¹⁰;

5) a-3a-2+ a-1a3+ a2+ a = a-3(1+a+ a2)a(a2+ a+1) = a-8a = a^–4;

6) 6n+2- 6n35 – 6n(62- 1)35 = 6n • 3535 = 6ⁿ;

7) 5n+2- 5n-25n = 5n(52- 5-2)5n = 25 – 125 = 25 – 0,04 = 24,96;

8) 2-n+ 12n+ 1 = 2-n(1+ 2n)2n+ 1 = 2^–n. = 1+ 2n • 12n(2n+ 1) = 12n = 2^–n.