5) (-1 7/9)¹⁰ ⋅ (-1 7/9)¹² ∶ (-1 7/9)²⁰;

5) Сначала выполним умножение, затем деление.

$$\left(-\frac{16}{9}\right)^{10} \cdot \left(-\frac{16}{9}\right)^{12} = \left(-\frac{16}{9}\right)^{10+12} = \left(-\frac{16}{9}\right)^{22}$$.

$$\left(-\frac{16}{9}\right)^{22} : \left(-\frac{16}{9}\right)^{20} = \left(-\frac{16}{9}\right)^{22-20} = \left(-\frac{16}{9}\right)^2 = \left(\frac{256}{81}\right) = 3 \frac{13}{81}$$.

Ответ: 3 13/81