$a){13}^5\cdot {13}^6={13}^{5+6}={13}^{11}$  

$b){\left(-123\right)}^3\cdot {\left(-123\right)}^9={\left(-123\right)}^{3+9}={\left(-123\right)}^{12}$  

$c)6^{11}\cdot 6\cdot 6^{12}=6^{11+1+12}=6^{24}$  

$d)\frac{{\left(-17\right)}^9}{{\left(-17\right)}^4}={\left(-17\right)}^{9-4}={\left(-17\right)}^5$  

$e){\left(1\frac{1}{3}\right)}^{13}:1\frac{1}{3}={\left(1\frac{1}{3}\right)}^{13-1}={\left(1\frac{1}{3}\right)}^{12}$

$f)\frac{8^{14}\cdot 8^{16}}{8^{15}}=8^{14+16-15}=8^{30-15}=8^{15}$  

$g)\frac{a^9\cdot a^6}{a^4}=\frac{a^{9+6}}{a^4}=a^{15-4}=a^{11}$

$h)\frac{x^{11}\cdot x^5\cdot x}{x^{18}:x^9}=\frac{x\left(11+5+1\right)}{x^{18-9}}=x^{17-9}=x^8$

$i)\frac{b^7\cdot b^3:\left(b^2\cdot b\right)}{b^4\cdot b^2:b}=\frac{b^7\cdot b^3:b^{2+1}}{b^{4+2-1}}=\frac{b^{7+3-3}}{b^5}=b^{7-5}=b^2$