Answer:
The final answer is
.
Step-by-step explanation:
Solve the following equation:
![(2^{2} \cdot 3^{-1} \cdot 4^{-1})^{-1} \over 2^{-3} \cdot 3^{4}](https://tex.z-dn.net/?f=%282%5E%7B2%7D%20%5Ccdot%203%5E%7B-1%7D%20%5Ccdot%204%5E%7B-1%7D%29%5E%7B-1%7D%20%5Cover%202%5E%7B-3%7D%20%5Ccdot%203%5E%7B4%7D)
-Simplify
:
![(2^{2} \cdot 3^{-1} \cdot 4^{-1})^{-1} \over 2^{-3} \cdot 3^{4}](https://tex.z-dn.net/?f=%282%5E%7B2%7D%20%5Ccdot%203%5E%7B-1%7D%20%5Ccdot%204%5E%7B-1%7D%29%5E%7B-1%7D%20%5Cover%202%5E%7B-3%7D%20%5Ccdot%203%5E%7B4%7D)
![(4 \times 3^{-1} \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}](https://tex.z-dn.net/?f=%284%20%5Ctimes%203%5E%7B-1%7D%20%5Ctimes%204%5E%7B-1%7D%29%5E%7B-1%7D%20%5Cover%202%5E%7B-3%7D%20%5Ctimes%203%5E%7B4%7D)
-Simplify
:
![(4 \times 3^{-1} \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}](https://tex.z-dn.net/?f=%284%20%5Ctimes%203%5E%7B-1%7D%20%5Ctimes%204%5E%7B-1%7D%29%5E%7B-1%7D%20%5Cover%202%5E%7B-3%7D%20%5Ctimes%203%5E%7B4%7D)
![(4 \times( \frac{1}{3}) \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}](https://tex.z-dn.net/?f=%284%20%5Ctimes%28%20%5Cfrac%7B1%7D%7B3%7D%29%20%5Ctimes%204%5E%7B-1%7D%29%5E%7B-1%7D%20%5Cover%202%5E%7B-3%7D%20%5Ctimes%203%5E%7B4%7D)
-Multiply both
and
:
![(4 \times( \frac{1}{3}) \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}](https://tex.z-dn.net/?f=%284%20%5Ctimes%28%20%5Cfrac%7B1%7D%7B3%7D%29%20%5Ctimes%204%5E%7B-1%7D%29%5E%7B-1%7D%20%5Cover%202%5E%7B-3%7D%20%5Ctimes%203%5E%7B4%7D)
![(\frac{4}{3} \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}](https://tex.z-dn.net/?f=%28%5Cfrac%7B4%7D%7B3%7D%20%5Ctimes%204%5E%7B-1%7D%29%5E%7B-1%7D%20%5Cover%202%5E%7B-3%7D%20%5Ctimes%203%5E%7B4%7D)
-Simplify
:
![(\frac{4}{3} \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}](https://tex.z-dn.net/?f=%28%5Cfrac%7B4%7D%7B3%7D%20%5Ctimes%204%5E%7B-1%7D%29%5E%7B-1%7D%20%5Cover%202%5E%7B-3%7D%20%5Ctimes%203%5E%7B4%7D)
![(\frac{4}{3} \times (\frac{1}{4}) )^{-1} \over 2^{-3} \times 3^{4}](https://tex.z-dn.net/?f=%28%5Cfrac%7B4%7D%7B3%7D%20%5Ctimes%20%28%5Cfrac%7B1%7D%7B4%7D%29%20%29%5E%7B-1%7D%20%5Cover%202%5E%7B-3%7D%20%5Ctimes%203%5E%7B4%7D)
-Multiply both
and
together:
![(\frac{4}{3} \times (\frac{1}{4}) )^{-1} \over 2^{-3} \times 3^{4}](https://tex.z-dn.net/?f=%28%5Cfrac%7B4%7D%7B3%7D%20%5Ctimes%20%28%5Cfrac%7B1%7D%7B4%7D%29%20%29%5E%7B-1%7D%20%5Cover%202%5E%7B-3%7D%20%5Ctimes%203%5E%7B4%7D)
![(\frac{1}{3})^{-1} \over 2^{-3} \times 3^{4}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B-1%7D%20%5Cover%202%5E%7B-3%7D%20%5Ctimes%203%5E%7B4%7D)
-Simplify
:
![(\frac{1}{3})^{-1} \over 2^{-3} \times 3^{4}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B-1%7D%20%5Cover%202%5E%7B-3%7D%20%5Ctimes%203%5E%7B4%7D)
![3 \over 2^{-3} \times 3^{4}](https://tex.z-dn.net/?f=3%20%5Cover%202%5E%7B-3%7D%20%5Ctimes%203%5E%7B4%7D)
-Then, on the denominator, simplify
:
![3 \over 2^{-3} \times 3^{4}](https://tex.z-dn.net/?f=3%20%5Cover%202%5E%7B-3%7D%20%5Ctimes%203%5E%7B4%7D)
![3 \over \frac{1}{8} \times 3^{4}](https://tex.z-dn.net/?f=3%20%5Cover%20%5Cfrac%7B1%7D%7B8%7D%20%20%5Ctimes%203%5E%7B4%7D)
Simplify
:
![3 \over \frac{1}{8} \times 3^{4}](https://tex.z-dn.net/?f=3%20%5Cover%20%5Cfrac%7B1%7D%7B8%7D%20%20%5Ctimes%203%5E%7B4%7D)
![3 \over \frac{1}{8} \times 81](https://tex.z-dn.net/?f=3%20%5Cover%20%5Cfrac%7B1%7D%7B8%7D%20%20%5Ctimes%2081)
Multiply both
and
together:
![3 \over \frac{1}{8} \times 81](https://tex.z-dn.net/?f=3%20%5Cover%20%5Cfrac%7B1%7D%7B8%7D%20%20%5Ctimes%2081)
![3 \over \frac{81}{8}](https://tex.z-dn.net/?f=3%20%5Cover%20%5Cfrac%7B81%7D%7B8%7D)
Divide
and
by multiplying
by the reciprocal of
:
![3 \over \frac{81}{8}](https://tex.z-dn.net/?f=3%20%5Cover%20%5Cfrac%7B81%7D%7B8%7D)
![3 \times (\frac{81}{8})](https://tex.z-dn.net/?f=3%20%5Ctimes%20%28%5Cfrac%7B81%7D%7B8%7D%29)
-And you multiply
and
together:
![3 \times (\frac{81}{8})](https://tex.z-dn.net/?f=3%20%5Ctimes%20%28%5Cfrac%7B81%7D%7B8%7D%29)
![\frac{8}{27}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B27%7D)
So, the final answer would be
.