Answer:
The answers are A , C , D
Step-by-step explanation:
Lets revise the rule of exponent
* ![a^{n}*a^{m}=a^{m+n}](https://tex.z-dn.net/?f=a%5E%7Bn%7D%2Aa%5E%7Bm%7D%3Da%5E%7Bm%2Bn%7D)
* ![\frac{a^{m}}{a^{n}}=a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7Bm%7D%7D%7Ba%5E%7Bn%7D%7D%3Da%5E%7Bm-n%7D)
* ![\frac{1}{a^{-m}}=a^{m}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Ba%5E%7B-m%7D%7D%3Da%5E%7Bm%7D)
* ![(\frac{a}{b})^{-m}=(\frac{b}{b})^{m}](https://tex.z-dn.net/?f=%28%5Cfrac%7Ba%7D%7Bb%7D%29%5E%7B-m%7D%3D%28%5Cfrac%7Bb%7D%7Bb%7D%29%5E%7Bm%7D)
Now lets solve the problem
We need all the expressions equivalent to ![\frac{1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D)
A.
∵ ![2^{-3}=\frac{1}{2^{3}}](https://tex.z-dn.net/?f=2%5E%7B-3%7D%3D%5Cfrac%7B1%7D%7B2%5E%7B3%7D%7D)
∵ 2³ = 8
∴ ![2^{-3}=\frac{1}{8}](https://tex.z-dn.net/?f=2%5E%7B-3%7D%3D%5Cfrac%7B1%7D%7B8%7D)
Answer A is equivalent to ![\frac{1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D)
B.
∵ 2³ = 8
Answer B is not equivalent to ![\frac{1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D)
C.
∵ 2³ = 8
∴ ![\frac{1}{2^{3}}=\frac{1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%5E%7B3%7D%7D%3D%5Cfrac%7B1%7D%7B8%7D)
Answer C is equivalent to ![\frac{1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D)
D.
∵ ![2^{2}*2^{-5}=2^{2+-5}=2^{-3}](https://tex.z-dn.net/?f=2%5E%7B2%7D%2A2%5E%7B-5%7D%3D2%5E%7B2%2B-5%7D%3D2%5E%7B-3%7D)
∵ ![2^{-3}=\frac{1}{2^{3}}=\frac{1}{8}](https://tex.z-dn.net/?f=2%5E%7B-3%7D%3D%5Cfrac%7B1%7D%7B2%5E%7B3%7D%7D%3D%5Cfrac%7B1%7D%7B8%7D)
Answer D is equivalent to ![\frac{1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D)
E.
∵ ![2^{-2}*2^{5}=2^{-2+5}=2^{3}](https://tex.z-dn.net/?f=2%5E%7B-2%7D%2A2%5E%7B5%7D%3D2%5E%7B-2%2B5%7D%3D2%5E%7B3%7D)
∵ 2³ = 8
Answer E is not equivalent to ![\frac{1}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D)
<em>The answers are A , C , D</em>