Step 1 :Multiply the numbers: \(5.4 \times 1.8 \times 4.2 = 40.824\)
Step 2 :Add the exponents: \(-6 + -6 + 7 = -5\)
Step 3 :Convert to scientific notation: \(40.824 \times 10^{-5} = 4.0824 \times 10^{-4}\)
Step 4 :Round to three significant digits: \(4.0824 \times 10^{-4} = 4.082 \times 10^{-4}\)
Step 5 :\(\boxed{4.082 \times 10^{-4}}\)