Question

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

• A. ${\left(3^3\right)}^2$
• B. $3^9$
• C. $3^6$
• D. $3^3$ × $3^3$

Answer 1

The correct option is B

$3^9$

As ${\left(a^m\right)}^n$ = $a^{m\times n}$

${\left(3^2\right)}^3$ = $3^{2\times 3}$ = $3^6$

${\left(3^3\right)}^2$ = $3^{2\times 3}$ = $3^6$

$3^3\times 3^3=3^{3+3}=3^6[\because a^m\times a^n=a^{m+n}]$

Since $3^9\ne 3^6$, therefore $3^9\ne {\left(3^2\right)}^3$.