Answer:
Option E.
Step-by-step explanation:
The given expression is
[tex]\frac{(ab)^3}{(3a)^2b}[/tex]
We need to find the simplified form of the given expression.
Using the distributive property of exponent we get
[tex]\frac{a^3b^3}{(3)^2a^2b}[/tex] [tex][\becasue (ab)^x=a^xb^x][/tex]
[tex]\frac{a^3b^3}{9a^2b}[/tex]
Using the quotient property of exponent we get
[tex]\frac{a^{3-2}b^{3-1}}{9}[/tex] [tex][\becasue \frac{a^m}{a^n}=a^{m-n}][/tex]
[tex]\frac{a^{1}b^{2}}{9}[/tex]
[tex]\frac{ab^{2}}{9}[/tex]
The simplified form of the given expression is [tex]\frac{ab^{2}}{9}[/tex].
Therefore, the correct option is E.
