2. Упростите выражение: a) 1,6x⁻⁶y¹⁰ ⋅ 15x³y⁻⁴; б) (\(\frac{3a^3}{2b^{-5}}\))⁻².

Решение:

• а) 1,6x⁻⁶y¹⁰ ⋅ 15x³y⁻⁴ = (1,6 ⋅ 15) ⋅ (x⁻⁶ ⋅ x³) ⋅ (y¹⁰ ⋅ y⁻⁴) = 24 ⋅ x^(-6+3) ⋅ y^(10-4) = 24x⁻³y⁶ = \(\frac{24y^6}{x^3}\)
• б) (\(\frac{3a^3}{2b^{-5}}\))⁻² = (\(\frac{2b^{-5}}{3a^3}\))² = \(\frac{(2b^{-5})^2}{(3a^3)^2}\) = \(\frac{4b^{-10}}{9a^6}\) = \(\frac{4}{9a^6b^{10}}\)

Ответ: а) \(\frac{24y^6}{x^3}\); б) \(\frac{4}{9a^6b^{10}}\).