$a){100}^9={\left({10}^2\right)}^9={10}^{2\cdot 9}={10}^{18}$

${1000}^7={\left({10}^3\right)}^7={10}^{3\cdot 7}={10}^{21}$

$100{000}^{11}={\left({10}^5\right)}^{11}={10}^{5\cdot 11}={10}^{55}$

$b){0,01}^4={\left({0,1}^2\right)}^4={0,1}^{2\cdot 4}={0,1}^8$  

${0,001}^9={\left({0,1}^3\right)}^9={0,1}^{3\cdot 9}={0,1}^{27}$

${0,00001}^8={\left({0,1}^5\right)}^8={0,1}^{5\cdot 8}={0,1}^{40}$