Вправи: 282

282. Виконайте дії та зведіть отриманий вираз до вигляду, який не містить степеня з від’ємним показником:

1) –2,4a^–4b³ • (–2a^–3c^–5)^–3 = –2,4a^–4b³ • (–2)^–3a⁹c¹⁵ = 2,4 • (–18)a⁵b¹⁸ = –0,3a⁵b¹⁸;

2) (–10x^–2yz^–8)^–2 • (0,1yx^–4)^–2 = (–10)^–2x⁴y^–2z¹⁶ • (110)^–2y^–2z⁸ = (–10 • 110)^–2x⁴y^–4z²⁴ = x4z24y4;

3) 179m^–6n • (113m^–1n^–4)^–3 = 169 • m^–6n • (43)^–3 m³n¹² = 169 • (34)³ m^–3n¹³ = 16 • 279 • 64m^–3n¹³ = 3n134m3;

4) (–16a^–3b^–6)^–3 • (–6a²b⁹)^–2 = (–16)^–3a⁹b¹⁸ • (–6)^–2a^–4b^–18 = –6³ • 6^–2a⁵b⁰ = –6a⁵;

5) (7p-35k-1)^–2 • 49m^–6n⁴ = (5k-17p-3)² • 49m^–6n⁴ = 25k-2 • 49m-6n449p-3 = 25n4p6k2m6;

6) (4x-53y-2)^–3 • (16x^–6y⁴)² = (3y-24x-5)³ • 256x^–12y⁸ = 27y-6 • 256x-12y864 • x-15 = 108x12y2x-15 = 108x³y².