6. Упростите выражение: a) (-2\(\frac{1}{2}\)a³b)⁴ ∙ 3\(\frac{1}{5}\)a⁸b⁵; б) x²ⁿ : (xⁿ⁻¹)².

6. Упростим выражение:

a) (-2\(\frac{1}{2}\)a³b)⁴ ∙ 3\(\frac{1}{5}\)a⁸b⁵ = (-\(\frac{5}{2}\)a³b)⁴ * \(\frac{16}{5}\)a⁸b⁵ = (\(\frac{5}{2}\))⁴ * a^(3*4) * b⁴ * \(\frac{16}{5}\)a⁸b⁵ = (\(\frac{625}{16}\)) * a¹² * b⁴ * \(\frac{16}{5}\)a⁸b⁵ = \(\frac{625}{16}\) * \(\frac{16}{5}\) * a^(12+8) * b^(4+5) = 125a²⁰b⁹

б) x²ⁿ : (xⁿ⁻¹)² = x²ⁿ : x^(2*(n-1)) = x²ⁿ : x^(2n-2) = x^(2n - (2n-2)) = x^(2n - 2n + 2) = x²

Ответ: а) 125a²⁰b⁹; б) x²