Note: Consider the given figure attached with this question.
Given:
The expression is:
![2^5\times 2^4](https://tex.z-dn.net/?f=2%5E5%5Ctimes%202%5E4)
To find:
The equivalent expression.
Solution:
We have,
![2^5\times 2^4](https://tex.z-dn.net/?f=2%5E5%5Ctimes%202%5E4)
It can be written as:
![2^5\times 2^4=2^{5+4}](https://tex.z-dn.net/?f=2%5E5%5Ctimes%202%5E4%3D2%5E%7B5%2B4%7D)
![2^5\times 2^4=2^{9}](https://tex.z-dn.net/?f=2%5E5%5Ctimes%202%5E4%3D2%5E%7B9%7D)
So, option A is correct and option B is incorrect.
Similarly, in options C, D, E,
![2\cdot 2^9=2^{10}](https://tex.z-dn.net/?f=2%5Ccdot%202%5E9%3D2%5E%7B10%7D)
![2^{10}\cdot 2^2=2^{12}](https://tex.z-dn.net/?f=2%5E%7B10%7D%5Ccdot%202%5E2%3D2%5E%7B12%7D)
![2^{-2}\cdot 2^{11}=2^{9}](https://tex.z-dn.net/?f=2%5E%7B-2%7D%5Ccdot%202%5E%7B11%7D%3D2%5E%7B9%7D)
So, options C and D are incorrect but option E is correct.
The given expression can be written as:
![(2\cdot 2\cdot 2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2\cdot 2)](https://tex.z-dn.net/?f=%282%5Ccdot%202%5Ccdot%202%5Ccdot%202%5Ccdot%202%29%5Ccdot%20%282%5Ccdot%202%5Ccdot%202%5Ccdot%202%29)
So, option F is correct.
Therefore, the correct options are A, E F.