Answer:
[tex]3^{\frac{1}{6} }[/tex]
Step-by-step explanation:
Using the rules of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
Evaluating the parenthesis, gives
[tex]\frac{3^{\frac{3}{4} } }{3^{\frac{3}{8} } }[/tex] = [tex]3^{\frac{3}{4}-\frac{3}{8} }[/tex] = [tex]3^{\frac{3}{8} }[/tex] , then
[tex](3^{\frac{3}{8})^{\frac{4}{9} } }[/tex] → [tex]\frac{3}{8}[/tex] × [tex]\frac{4}{9}[/tex] = [tex]\frac{1}{6}[/tex]
= [tex]3^{\frac{1}{6} }[/tex] with x = [tex]\frac{1}{6}[/tex]
