Answer:
3rd option
Step-by-step explanation:
using the rules of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] : nm > n
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex] : n > m
[tex]\frac{6a^2b^{-2} }{8a^{-3b^3} }[/tex] ← separate the variables
= [tex]\frac{6}{8}[/tex] × [tex]\frac{a^2}{a^{-3} }[/tex] × [tex]\frac{b^{-2} }{b^3}[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{2-(-3)}[/tex] × [tex]\frac{1}{b^{3-(-2)} }[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{2+3}[/tex] × [tex]\frac{1}{b^{3+2} }[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{5}[/tex] × [tex]\frac{1}{b^{5} }[/tex]
= [tex]\frac{3a^{5} }{4b^{5} }[/tex]
