Упростите выражение: a) 5ab^-5 ⋅ 0,4a^-3b⁸; б) (0,3p⁶q^-1)^-2

Решение:

• a) 5ab^-5 ⋅ 0,4a^-3b⁸ = (5 ⋅ 0,4) ⋅ (a ⋅ a^-3) ⋅ (b^-5 ⋅ b⁸) = 2 ⋅ a^1+(-3) ⋅ b^-5+8 = 2a^-2b³ = \(\frac{2b^3}{a^2}\).
• б) (0,3p⁶q^-1)^-2 = (0,3)^-2 ⋅ (p⁶)^-2 ⋅ (q^-1)^-2 = \(\left(\frac{3}{10}\right)^{-2}\) ⋅ p^6⋅(-2) ⋅ q^(-1)⋅(-2) = \(\left(\frac{10}{3}\right)^{2}\) ⋅ p^-12 ⋅ q² = \(\frac{100}{9}\) ⋅ \(\frac{1}{p^{12}}\)⋅q² = \(\frac{100q^2}{9p^{12}}\).

Ответ: а) \(\frac{2b^3}{a^2}\), б) \(\frac{100q^2}{9p^{12}}\)