Question

If $[3^{m^2}÷(3^m{)}^2{]}^{\frac{1}{8}}=81$, the value of $m$ is _____

• A. $3$
• B. $6$
• C. $-3$
• D. $-6$
• E. $Noneofthese$

Answer 1

Answer: (B)

$6$

$[3^{m^2}÷(3m{)}^2{]}^{1/m}=87$

$\Rightarrow (3^{m^2}÷3^{2m}{)}^{1/m}=3^4$

$\Rightarrow (3^{m^2-2m}{)}^{1/m}=3^4$

$\Rightarrow 3^{m^2-23}=3^4$

Since basses are same, so we have

$\Rightarrow \frac{m^2-2m}{m}=4$

$m^2-2m-4m=0$

$m^2-6m$

$m(m-6)=0m=6$

Option $B$ is correct.