Question

The value of m if :
$4^{2m}=(3\sqrt{16}{)}^{-\frac{6}{n}}=(\sqrt{8}{)}^2$ is $m=\frac{3}{4}$
If true then enter $1$ and if false then enter $0$

• A. True
• B. False

Answer 1

The correct option is A True

As given$\Rightarrow 4^{2m}=(3\sqrt{16}{)}^{-\frac{6}{n}}=(\sqrt{8}{)}^2$
$\Rightarrow {\left(2^2\right)}^{2m}={\left({\left(2^4\right)}^{\frac{1}{3}}\right)}^{-\frac{6}{n}}={\left({\left(2^3\right)}^{\frac{1}{2}}\right)}^2$
$\Rightarrow 2^{4m}={\left(2^{\frac{4}{3}}\right)}^{-\frac{6}{n}}={\left(2^{\frac{3}{2}}\right)}^2$
$\Rightarrow 2^{4m}=2^{\frac{4}{3}.-\frac{6}{n}}=2^{\frac{3}{2}.2}$
$\Rightarrow 2^{4m}=2^{-\frac{8}{n}}=2^3$
$\Rightarrow 2^{4m}=2^3$
$\Rightarrow 4m=3\Rightarrow m=\frac{3}{4}$
$\Rightarrow 2^{-\frac{8}{n}}=2^3$
$\Rightarrow -\frac{8}{n}=3\Rightarrow n=-\frac{8}{3}$
$\Rightarrow m=\frac{3}{4}n=-\frac{8}{3}$