а) $$ a^5 \cdot a^8 = a^{5+8} = a^{13} $$
б) $$ a^8 : a^3 = a^{8-3} = a^5 $$
в) $$(a^5)^8 = a^{5 \cdot 8} = a^{40}$$
г) $$\frac{(a^3)^2 \cdot a^{15}}{a^{17}} = \frac{a^{3 \cdot 2} \cdot a^{15}}{a^{17}} = \frac{a^6 \cdot a^{15}}{a^{17}} = \frac{a^{6+15}}{a^{17}} = \frac{a^{21}}{a^{17}} = a^{21-17} = a^4$$