Question

If $9^{1/2}\times 3^m=(27{)}^m$, then the value of m is :

• A. 1/4
• B. 1/5
• C. 1/3
• D. 1/2

Answer 1

The correct option is D 1/2

$9^{1/2}\times 3^m=(27{)}^m$

$\Rightarrow (3^2{)}^{1/2}\times 3^m=3^{3m}$

$\Rightarrow 3\times 3^m=3^{3m}$

$3^{m+1}=3^{3m}$

$\Rightarrow m+1=3m\Rightarrow m=1/2$