a) ${15}^2:15={15}^2:{15}^1={15}^{2-1}={15}^1=15$

b) $\frac{4^{180}}{4^{177}}=4^{180-177}=4^3=64$

c) $\frac{5^8\cdot 5^9}{5^{15}}=\frac{5^{8+9}}{5^{15}}=\frac{5^{17}}{5^{15}}=5^{17-15}=5^2=25$