a) \( \left(\frac{1}{3}\right)^{-3} \times(3)^{-1} \times \frac{1}{9} \)

To simplify the expression \( \left(\frac{1}{3}\right)^{-3} \times(3)^{-1} \times \frac{1}{9} \), we start with the first term: - \( \left(\frac{1}{3}\right)^{-3} = 3^3 = 27 \) Now, we tackle the second term: - \( (3)^{-1} = \frac{1}{3} \) Now we rewrite \( \frac{1}{9} \): - \( \frac{1}{9} = \frac{1}{3^2} \) Now, substituting in, we have: \[ 27 \times \frac{1}{3} \times \frac{1}{3^2} \] This simplifies to: \[ 27 \times \frac{1}{3^{1 + 2}} = 27 \times \frac{1}{3^3} \] Since \( 3^3 = 27 \), we can combine it: \[ 27 \times \frac{1}{27} = 1 \] So the final result is: \[ 1 \]