Question

(2^2m)^3/(2^3m)^4=2^4m-12 find value of m​

Answer 1

Answer:

The answer is  $m=\dfrac{6}{5}$

Step-by-step explanation:

Given equation is

   $\dfrac{(2^{2m})^3}{(2^{3m})^4}=2^{4m-12}$

$\Rightarrow \dfrac{2^{2m\times 3}}{2^{3m\times 4}}=2^{4m-12}$

$\Rightarrow \dfrac{2^{6m}}{2^{12m}}=2^{4m-12}\\\\\Rightarrow {2^{6m-12m}}=2^{4m-12}\\\\\Rightarrow {2^{-6m}}=2^{4m-12}\\\\\Rightarrow -6m=4m-12\\\Rightarrow 12=4m+6m=10m\\\Rightarrow m=\dfrac{12}{10}=\dfrac{6}{5}$

Answer 2

Step-by-step explanation:

Given equation is

\dfrac{(2^{2m})^3}{(2^{3m})^4}=2^{4m-12}

(2

3m

)

4

(2

2m

)

3

=2

4m−12

\Rightarrow \dfrac{2^{2m\times 3}}{2^{3m\times 4}}=2^{4m-12}⇒

2

3m×4

2

2m×3

=2

4m−12

\begin{gathered}\Rightarrow \dfrac{2^{6m}}{2^{12m}}=2^{4m-12}\\\\\Rightarrow {2^{6m-12m}}=2^{4m-12}\\\\\Rightarrow {2^{-6m}}=2^{4m-12}\\\\\Rightarrow -6m=4m-12\\\Rightarrow 12=4m+6m=10m\\\Rightarrow m=\dfrac{12}{10}=\dfrac{6}{5}\end{gathered}

⇒

2

12m

2

6m

=2

4m−12

⇒2

6m−12m

=2

4m−12

⇒2

−6m

=2

4m−12

⇒−6m=4m−12

⇒12=4m+6m=10m

⇒m=

10

12

=

5

6