Question

Which of the following is not equal to \({(3^{2})}^{3}\) ?

Answer 1

As \({(a^{m})}^{n}\) = \(a^{m×n}\)

\({(3^{2})}^{3}\) = \(3^{2 \times 3}\) = \(3^{6}\)

\({(3^{3})}^{2}\) = \(3^{2 \times 3}\) = \(3^{6}\)

\(3^{3} × 3^{3}= 3^{3+3} = 3^{6} ~~[ \because a^{m}× a^{n} = a^{m+n}]\)

Since \(3^{9} \neq 3^6\), therefore \(3^{9}\neq {(3^2)}^3\).