$a){\left(\frac{2}{3}\right)}^3\cdot {\left(\frac{2}{3}\right)}^2={\left(\frac{2}{3}\right)}^{3+2}={\left(\frac{2}{3}\right)}^5$

$b){\left(3^3\cdot 2^3\right)}^2={\left({\left(3\cdot 2\right)}^3\right)}^2={\left(6^3\right)}^2=6^{3\cdot 2}=6^6$ $b){\left(3^3\cdot 2^3\right)}^2={\left({\left(3\cdot 2\right)}^3\right)}^2={\left(6^3\right)}^2=6^{3\cdot 2}=6^6$

$c){\left(3^2\right)}^4=3^{2\cdot 4}=3^8$

$d){\left(\frac{2}{7}\right)}^5\cdot 7^5={\left(\frac{2}{7}\cdot 7\right)}^5=2^5$

$e){1,5}^8:{1,5}^3={1,5}^{8-3}={1,5}^5$

$f){2,5}^{10}:{25}^{10}={\left(2,5:25\right)}^{10}={\left(25:250\right)}^{10}={\left(\frac{25}{250}\right)}^{10}={\left(\frac{1}{10}\right)}^{10}={0,1}^{10}$