Answer:
When using the order of operations to solve the problem, then the final answer will be [tex]\frac{32}{9}[/tex]
Step-by-step explanation:
[tex](\frac{4}{9})^2[/tex] ÷ [tex](\frac{1}{3} +\frac{2}{9} -\frac{1}{2} )[/tex]
Following the order of operations, the first thing we have to do is add 1/3 to 2/9 and then subtract that sum by 1/2.
[tex](\frac{4}{9})^2[/tex] ÷ [tex](\frac{5}{9} -\frac{1}{2} )[/tex]
[tex](\frac{4}{9} )^2[/tex] ÷ [tex](\frac{1}{18} )[/tex]
Next, we solve the exponent on 4/9 by multiplying 4/9 with itself.
[tex](\frac{4}{9})^2= \frac{16}{81}[/tex]
[tex](\frac{16}{81} )[/tex] ÷ [tex](\frac{1}{18} )[/tex]
Lastly, we divide 16/81 by 1/18.
[tex](\frac{16}{81} )[/tex] ÷ [tex](\frac{1}{18} )[/tex] = [tex]\frac{32}{9}[/tex]
Since this number can not be simplified into a smaller fraction, then the answer will stay as it is.
So, your final answer will be [tex]\frac{32}{9}[/tex]
