The relevant rules of exponents are
[tex] x^{a}\cdot x^{b}=x^{(a+b)}\\\\\left(x^{a}\right)^{b}=x^{(a\cdot b)}\\\\x^{-a}=\dfrac{1}{x^{a}} [/tex]
1. [tex] \dfrac{\left(8^{3}\right)^{4}\cdot 8^{-9}}{8^{3}}=8^{(3\cdot 4-9-3)}=8^{0}=1[/tex]
2. [tex]\dfrac{8^{3}\cdot 8^{4}}{\left(8^{2}\right)^{4}}=8^{(3+4-2\cdot 4)}=8^{-1}[/tex]
