Answer:
a - b = 9
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m-n}[/tex] , then
[tex]\frac{2^{a} }{2^{b} }[/tex] = [tex]2^{a-b}[/tex] , so
[tex]2^{a-b}[/tex] = 512 = [tex]2^{9}[/tex]
since bases on both sides are equal, both 2 then equate exponents
a - b = 9
