6. Преобразуйте выражение (\(\frac{5}{6}a^{-4}b^{-5}\))⁻³ ⋅ (6a¹⁵b⁶)⁻² так, чтобы оно не содержало степеней с отрицательными показателями.

Ответ: \(\frac{216}{25}\) ⋅ \(\frac{1}{a^{18}b^3}\)

Преобразуем выражение:

((\(\frac{5}{6}\)a⁻⁴b⁻⁵)⁻³ ⋅ (6a¹⁵b⁶)⁻² = (\(\frac{5}{6}\))⁻³ ⋅ (a⁻⁴)⁻³ ⋅ (b⁻⁵)⁻³ ⋅ 6⁻² ⋅ (a¹⁵)⁻² ⋅ (b⁶)⁻² = (\(\frac{6}{5}\))³ ⋅ a¹² ⋅ b¹⁵ ⋅ (\(\frac{1}{6}\))² ⋅ a⁻³⁰ ⋅ b⁻¹² = (\(\frac{6}{5}\))³ ⋅ (\(\frac{1}{6}\))² ⋅ a¹²⁻³⁰ ⋅ b¹⁵⁻¹² = (\(\frac{6}{5}\))³ ⋅ (\(\frac{1}{6}\))² ⋅ a⁻¹⁸ ⋅ b³ = \(\frac{216}{125}\) ⋅ \(\frac{1}{36}\) ⋅ \(\frac{1}{a^{18}}\) ⋅ b³ = \(\frac{6}{125}\) ⋅ \(\frac{1}{a^{18}}\) ⋅ b³ = \(\frac{216}{25}\) ⋅ (\(\frac{1}{a^{18}b^3}\))

Ответ: \(\frac{216}{25}\) ⋅ \(\frac{1}{a^{18}b^3}\)