Answer
\[\frac{-79}{4}\].
Work Step by Step
Use rules of operations to find the value of the given expression.
Evaluate the parentheses first from left to right followed by division as:
\[\begin{align}
& \frac{1}{4}-6\left( 2+8 \right)\div \left( \frac{-1}{3} \right)\left( \frac{-1}{9} \right)=\frac{1}{4}-\frac{6\left( 10 \right)}{\frac{-1}{3}}\left( \frac{-1}{9} \right) \\
& =\frac{1}{4}-6\times 10\times -3\times \frac{-1}{9} \\
& =\frac{1}{4}-20
\end{align}\]
Now, perform the subtraction operation as:
\[\begin{align}
& \frac{1}{4}-20=\frac{1-80}{4} \\
& =\frac{-79}{4}
\end{align}\]
Hence, the value of \[\frac{1}{4}-6\left( 2+8 \right)\div \left( \frac{-1}{3} \right)\left( \frac{-1}{9} \right)\]is \[\frac{-79}{4}\].
