Question

Simplify: \((27)^{\frac{-1}{3}} \times (27)^{\frac{-1}{3}} \times [27^{\frac{1}{3}} - 27^{\frac{2}{3}}]\)

• A. \(-\frac{2}{3}\)
• B. 6
• C. \(-2\)
• D. 54

Hint:

\(a^{m} \times a^{n} = a^{m+n}\)

Answer 1

The Correct Option is A

Step 1: Simplify \(27^{\frac{-1}{3}}\). 
\(27^{\frac{1}{3}} = 3\), so \(27^{\frac{-1}{3}} = \frac{1}{3}\). 
Step 2: Multiply the first two factors. 
\(\frac{1}{3} \times \frac{1}{3} = \frac{1}{9}\). 
Step 3: Simplify the bracket. 
\(27^{\frac{1}{3}} = 3\). 
\(27^{\frac{2}{3}} = (27^{\frac{1}{3}})^2 = 3^2 = 9\). 
Bracket = \(3 - 9 = -6\). 
Step 4: Multiply. 
\(\frac{1}{9} \times (-6) = -\frac{6}{9} = -\frac{2}{3}\).