Answer:
The answers are A , C , D
Step-by-step explanation:
Lets revise the rule of exponent
* [tex]a^{n}*a^{m}=a^{m+n}[/tex]
* [tex]\frac{a^{m}}{a^{n}}=a^{m-n}[/tex]
* [tex]\frac{1}{a^{-m}}=a^{m}[/tex]
* [tex](\frac{a}{b})^{-m}=(\frac{b}{b})^{m}[/tex]
Now lets solve the problem
We need all the expressions equivalent to [tex]\frac{1}{8}[/tex]
A.
∵ [tex]2^{-3}=\frac{1}{2^{3}}[/tex]
∵ 2³ = 8
∴ [tex]2^{-3}=\frac{1}{8}[/tex]
Answer A is equivalent to [tex]\frac{1}{8}[/tex]
B.
∵ 2³ = 8
Answer B is not equivalent to [tex]\frac{1}{8}[/tex]
C.
∵ 2³ = 8
∴ [tex]\frac{1}{2^{3}}=\frac{1}{8}[/tex]
Answer C is equivalent to [tex]\frac{1}{8}[/tex]
D.
∵ [tex]2^{2}*2^{-5}=2^{2+-5}=2^{-3}[/tex]
∵ [tex]2^{-3}=\frac{1}{2^{3}}=\frac{1}{8}[/tex]
Answer D is equivalent to [tex]\frac{1}{8}[/tex]
E.
∵ [tex]2^{-2}*2^{5}=2^{-2+5}=2^{3}[/tex]
∵ 2³ = 8
Answer E is not equivalent to [tex]\frac{1}{8}[/tex]
The answers are A , C , D
