[tex]\Large\boxed{\begin{array}{l}\tt b)~\sf\dfrac{(a^2)^5\cdot(b^3)^3}{a^{-4}\cdot b^{-3}}\\\\\sf\dfrac{a^{10}\cdot b^9}{a^{-4}\cdot b^{-3}}=a^{10+4}\cdot b^{9+3}\\\\\sf\dfrac{(a^2)^5\cdot (b^3)^3}{a^{-4}\cdot b^{-3}}=a^{14}\cdot b^{12}\blue{\checkmark}\end{array}}[/tex]
[tex]\Large\boxed{\begin{array}{l}\tt b)~\sf\bigg(\dfrac{a}{b}\bigg)^8\cdot\dfrac{b^{10}}{a\cdot a^2\cdot a^3}\\\\\sf\dfrac{a^8}{b^8}\cdot\dfrac{b^{10}}{a^{1+2+3}}=\dfrac{a^8}{b^8}\cdot\dfrac{b^{10}}{a^6}\\\\\sf\dfrac{a^8\cdot b^{10}}{a^6\cdot b^8}=a^{8-6}\cdot b^{10-8}\\\\\sf\bigg(\dfrac{a}{b}\bigg)^8\cdot\dfrac{b^{10}}{a\cdot a^2\cdot a^3}=a^2\cdot b^2=(ab)^2\blue{\checkmark}\end{array}}[/tex]
