Решение:

a) $$rac{2^5 \cdot (2^3)^4}{2^{13}} = rac{2^5 \cdot 2^{3 \cdot 4}}{2^{13}} = rac{2^5 \cdot 2^{12}}{2^{13}} = rac{2^{5+12}}{2^{13}} = rac{2^{17}}{2^{13}} = 2^{17-13} = 2^4 = 16$$

Ответ: 16

б) $$\frac{(5^8)^2 \cdot 5^7}{5^{22}} = \frac{5^{8 \cdot 2} \cdot 5^7}{5^{22}} = \frac{5^{16} \cdot 5^7}{5^{22}} = \frac{5^{16+7}}{5^{22}} = \frac{5^{23}}{5^{22}} = 5^{23-22} = 5^1 = 5$$

Ответ: 5