Answer:
3/11
Step-by-step explanation:
Lets break down the equation into 2 halves.
[tex](\frac{27}{1331} )^{\frac{2}{3} }[/tex] is the first part.
This is asking for the square of the cube root of whatever is in the parenthesis.
Lets take the cube root first:
[tex]\sqrt[3]{\frac{27}{1331} } = \sqrt[3]{\frac{3^{3} }{11^{3} } } = \frac{3}{11}[/tex]
Now lets square it:
[tex](\frac{3}{11} )^{2} = \frac{9}{121}[/tex]
Now lets look at the second half - [tex](\frac{121}{9} )^{\frac{1}{2} }[/tex]
We are taking the square root of this value (thats what to the power of 1/2 means.)
[tex]\sqrt{\frac{121}{9} }=\frac{11}{3}[/tex]
Now we use algebra and multiply:
[tex]\frac{9}{121} *\frac{11}{3} = \frac{3}{11}[/tex]
Thus, the final answer is 3/11
