1) \(\dfrac{\left(2^{\frac35}\cdot5^{\frac23}\right)^{15}}{10^9}\)

Используем правило \((a^m)^n=a^{mn}\):

\[\dfrac{\left(2^{\frac35}\cdot5^{\frac23}\right)^{15}}{10^9}=\dfrac{2^9\cdot5^{10}}{(2\cdot5)^9}=\dfrac{2^9\cdot5^{10}}{2^9\cdot5^9}=5.\]

Ответ: 5.